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The Department of Homeland Security's

**National Infrastructure Simulation & Analysis Center**

*Managed by the Office of Infrastructure Protection*

*and*

**Critical Infrastructure Protection Decision Support System**

*Managed by the Infrastructure/Geophysical Division*

**Design of Community Containment for Pandemic Influenza with
Loki-Infect**

Robert Glass, Jason Min, Walt Beyeler

National Infrastructure Simulation and Analysis Center

Sandia National Laboratories

Albuquerque, New Mexico 87185

Laura Glass

Albuquerque Public High School

Albuquerque, New Mexico

**January 25, 2007**

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[]{#__RefHeading___Toc158828204 .anchor}Executive Summary

We have applied a community scale model that simulates the spread of
influenza in an explicit, multiply overlapping network of social
contacts within a stylized community. The modeled community can be
isolated or embedded within a regional epidemic where other communities
are either imposing the same containment strategies or doing nothing to
abate the epidemic. By focusing on a single community, we have been able
to evaluate an extensive matrix of containment strategy combinations and
disease infectivity levels. This exploration has enabled us to identify
community containment strategies that minimize illness, death, and loss
of workforce in the face of constrained antiviral or pre-pandemic
vaccine supplies. Building on this foundation, we have assessed the
robustness of containment designs to variations in disease
manifestation, social network configuration, strategy implementation
threshold, public compliance, and neighboring community behavior. Based
on the findings of this study, we summarize recommendations for policy
in three areas: 1) requirements of robust effective community
containment, 2) necessity of uniform national policy, and 3)
administration of pre-pandemic vaccine. Summary recommendations are also
made for the continued evaluation and reduction of uncertainty.

For a 1918-like pandemic infectivity level, strategies can be found that
are effective both at minimizing illness to below 5% of the population
(with nearly no deaths) using only the levels of antiviral coverage
currently within US stockpiles, and at limiting cost in terms of adult
days spent at home to below a week. These strategies are robust to both
changes in the social contact network that remove enhanced transmission
by children and teenagers and to changes in the disease manifestation
within the range currently used in modeling studies found in the
literature. However, strategy effectiveness depends on rapid
implementation and a high degree of public compliance both for social
distancing measures and antiviral treatment and home prophylaxis. The
latter encompasses both administration of antiviral drugs by the health
care infrastructure and use by the affected persons within the
population.

We find the most important component of effective strategy combinations
to be the implementation of social distancing with high compliance. For
an infectivity similar to that of the 1918 pandemic, administration of
antiviral prophylaxis at levels above 2% coverage adds no benefit and
does not remove the necessity of implementing high compliance social
distancing which includes closing schools. Closing schools imposes the
largest cost in days adults are at home. However, containment strategies
that combine closing schools *and* implementing social distancing of
children and teens are very effective when layered with home antiviral
prophylaxis. By adding implementation of social distancing by adults and
seniors (including a 50% reduction in contacts at work), adult days at
home can be minimized to an average of 6 per adult.

Thus, social distancing forms the foundation for effective community
containment. Alone it may be able to hold a pandemic at bay; in
combination with case based strategies such as home prophylaxis, death
and days adults are at home can be minimized. But we restate: strategies
must be implemented quickly and with high compliance. The *first*
*critical recommendation for policy* is that planning, education, and
training must be designed for the effective triggering and
implementation of high compliance social distancing measures *first* and
case-based strategies *second*. This conclusion contradicts the emphasis
within the medical and public health community over the past years where
antiviral prophylaxis has been the primary consideration. An important
component for high compliance social distancing among children will be
societal support of families with young children as they will bear the
vast majority of the costs of adult days at home. Such a redistribution
of burden could be accomplished through mechanisms including private
(company business plans, insurance policies), public (community
organization, taxation), and not-for-profit resources.

Isolated communities implementing effective community containment
strategies and communities embedded within regions implementing
effective community containment strategies perform identically. However,
our simulations in which communities implementing containment strategies
are embedded in a region that is doing nothing to abate the epidemic
("regionally unmitigated" with full contact through the work place) show
the importance of regional implementation of community containment
strategies. Without such regional policy, the best community containment
strategy (full social distancing layered with household antiviral
prophylaxis and 90% compliance) still reduces infectious attack rates
below 10%. However the attack and death rates quadruple from their
values for the regionally mitigated epidemic as do antiviral
requirements (to 9% coverage, well above the current stockpile of
oseltamivir of 7.2% in January, 2007), and the number of days adults are
at home are doubled. While the stockpile is set to grow to 25% by the
end of 2008, recent data from H5N1 cases in Egypt have shown that
resistance to oseltamivir is already developing. Thus, leaving
mitigation policy up to individual communities could cost the nation a
great deal. The *second* *critical recommendation for policy* is that a
*uniform national policy* should be imposed and supported for the
benefit of all.

Administration of pre-pandemic vaccination at proposed stockpile levels
(7% coverage and 50% efficacy) influences the spread of disease somewhat
when children and teens are targeted, as shown in our simulations to be
the most optimal focus. However, if the best community containment
strategy is implemented (full social distancing layered with household
antiviral prophylaxis and 90% compliance), pre-pandemic vaccine affords
no added benefit. Thus, the *third* *critical recommendation for policy*
is that pre-pandemic vaccine, if available at such low levels and
efficacy, should be used primarily to *assure that critical
infrastructures continue to function* during the period of the pandemic.
For highest community benefit, people in positions that cannot be
replaced in infrastructures which must remain operable (such as
healthcare and first responders) should be given the pre-pandemic
vaccine. The vaccine will both decrease the probability of them falling
ill and increase the probability of them continuing to work. Future
studies should consider if a stockpile size above the current proposed
7% coverage with 50% effective pre-pandemic vaccine would yield enough
benefit to change the choice of best community containment strategy.

As has been pointed out by the National Academy of Science's Institute
of Medicine recent review Modeling Community Containment for Pandemic
Influenza (IOM/NAS, 2006), much work remains to evaluate the uncertainty
of community containment efficacy. Simulation studies such as ours can
aid in evaluating uncertainty and in reducing this uncertainty over
time. The current study has taken a step forward along this path and
developed a base line set of results for evaluation. Future studies
should systematically consider parametric assumptions for the underlying
disease manifestations, social contact network, the action of antiviral
drugs, and containment strategy implementation. Modification of
community scale models and subsequent analytic sweeps of parameter space
are feasible to evaluate the uncertainty imposed by these assumptions.
Additionally, analysis can be refined in response to evolving
constraints and changes in uncertainty from data collected as new
influenza strains emerge and combined strategy implementations are
undertaken. Ongoing work in this area should include and *emphasize
community scale modeling* in addition to modeling at the regional or
national scales. Modeling activities at all scales should continue into
the indefinite future and work to fully integrate with economic analysis
and detection/monitoring systems for influenza.

[]{#__RefHeading___Toc158828205 .anchor}Acknowledgements

This research was supported by the National Infrastructure Simulation
and Analysis Center (NISAC), a program of the Department of Homeland
Security\'s Infrastructure Protection/Risk Management Division and
comprised of a core partnership of Sandia National Laboratories (SNL)
and Los Alamos National Laboratory (LANL). Many colleagues have
contributed to this work.

Richard Hatchett (NIH/NIAID), and Carter Mecher (VA) worked with the
senior author to define and frame the context for the studies contained
within this report.

Victoria Davey (VA) helped to formulate regionally mitigated and
unmitigated scenarios, and design effective criteria for rescinding
mitigation strategies that minimize illness, epidemic re-occurrence, and
social disruption.

Hillery Harvey (NIH/NIAID), Robert Taylor (NIH/NIAID) and Lone Simonsen
(NIH/NIAID) invited the use of preliminary results as part of the 2006
Discovery Channel Young Scientist Challenge hosted by NIH/NIAID and
helped to refine the results in a way that could be used by policy
makers (the young scientist's role in the Challenge).

Louise Maffitt (NISAC) provided constructive review of the manuscript.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a
Lockheed Martin Company for the United States Department of Energy's
National Nuclear Security Administration under contract
DE-AC04-94AL85000.

[]{#__RefHeading___Toc158828206 .anchor}Acronyms

AMTI Advanced Modeling Techniques Investigation

CDC Centers for Disease Control and Prevention

HHS Department of Health and Human Services

NISAC National Infrastructure Simulation and Analysis Center

CIPDSS Critical Infrastructure Protection Decision Support System

DHS Department of Homeland Security

WHHSC White House Homeland Security Council

PIP Pandemic Implementation Plan

MIDAS Models of Infectious Disease Agent Study (funded by National
Institute of General Medical Sciences of the National Institutes of
Health)

NIH National Institutes of Health

NIAID National Institute of Allergy and Infectious Diseases

TLC Targeted Layered Containment

VA Department of Veterans Affairs

[]{#__RefHeading___Toc158828207 .anchor}Symbols

*R~0~* Basic reproductive number of a disease defined as the average
number of people infected by a diseased individual in an entirely
susceptible population

*pS* Probability of symptomatic

*pH* Probability of staying at home if symptomatic

*pM* Probability of death if symptoms occur

*I~D\ ~*Infectivity of the disease

*I~R\ ~*Relative infectivity of the disease state

*I~A\ ~*Relative infectivity of the person who is transmitting

*S~P\ ~*Susceptibility of people to the disease

*S~A\ ~*Relative susceptibility of the person who is receiving

*\<I~R~\>* Weighted average of *I~A~* for adults over symptomatic
(reduced by diagnosis) and asymptomatic individuals for the mean
contagious period

*F* Current work group frequency scaling for a particular adult agent

IDfactor Multiplier on *I~D~* for systematic variation of disease
infectivity relative to a base

**TABLE OF CONTENTS**

[Executive Summary i](#__RefHeading___Toc158828204)

[Acknowledgements iv](#__RefHeading___Toc158828205)

[Acronyms iv](#__RefHeading___Toc158828206)

[Symbols v](#__RefHeading___Toc158828207)

[Table of Figures vii](#__RefHeading___Toc158828208)

[Table of Tables vii](#__RefHeading___Toc158828209)

[1 Introduction 1](#introduction)

[1.1 Programmatic Context 1](#programmatic-context)

[1.2 Accomplishments 1](#accomplishments)

[1.3 This Report 3](#this-report)

[2 Study Definition 4](#study-definition)

[3 Methods 6](#methods)

[3.1 Loki-Infect Model 6](#loki-infect-model)

[3.1.1 Contact Network 6](#contact-network)

[3.1.2 Behavioral Rules 8](#behavioral-rules)

[3.2 Specific Manifestations of Influenza
10](#specific-manifestations-of-influenza)

[3.3 Network of Infectious Contacts 11](#network-of-infectious-contacts)

[3.4 Choosing Disease Infectivity *I~D~*
12](#choosing-disease-infectivity-id)

[3.5 Instigation and Boundary Conditions
12](#instigation-and-boundary-conditions)

[3.6 Community Containment Strategies
13](#community-containment-strategies)

[4 Results 15](#results)

[4.1 Base Containment Strategy Combination Matrix for Ferguson-like
Disease Manifestation
15](#base-containment-strategy-combination-matrix-for-ferguson-like-disease-manifestation)

[4.1.1 90% compliance: 16](#compliance)

[4.1.2 60% compliance: 19](#compliance-1)

[4.1.3 External Contacts: 21](#external-contacts)

[4.2 Base Matrix Extensions 24](#base-matrix-extensions)

[4.2.1 Longini-like disease manifestation:
24](#longini-like-disease-manifestation)

[4.2.2 Relaxing Implementation Threshold:
30](#relaxing-implementation-threshold)

[4.2.3 Administering Pre-Pandemic Vaccine:
35](#administering-pre-pandemic-vaccine)

[4.2.4 Age Class Balanced Transmission:
40](#age-class-balanced-transmission)

[5 Design Of Effective, Robust Community Containment
45](#design-of-effective-robust-community-containment)

[5.1 Base design 45](#base-design)

[5.2 Pre-Pandemic Vaccination: 48](#pre-pandemic-vaccination)

[5.3 Robustness 52](#robustness)

[6 Recommendations For Policy 59](#recommendations-for-policy)

[6.1 Requirements of robust effective community containment strategies
59](#requirements-of-robust-effective-community-containment-strategies)

[6.2 Necessity of a Uniform National Policy
60](#necessity-of-a-uniform-national-policy)

[6.3 Administration of Pre-pandemic Vaccine
60](#administration-of-pre-pandemic-vaccine)

[6.4 Continued evaluation and reduction of uncertainty
61](#continued-evaluation-and-reduction-of-uncertainty)

[References 62](#__RefHeading___Toc158828243)

[Appendix A: Design of Targeted Social Distancing Strategies For
Pandemic Influenza 64](#__RefHeading___Toc158828245)

[Appendix B: WHHSC PIP Simulation Outline
65](#__RefHeading___Toc158828246)

[Appendix C: Unmitigated Base Case Analysis
66](#__RefHeading___Toc158828247)

[Appendix D: Base Containment Strategy Combination Matrix Results
71](#__RefHeading___Toc158828248)

[Appendix E: Matrix Extension Results 72](#OLE_LINK1)

[Appendix F: Presentation To The Institute Of Medicine
74](#__RefHeading___Toc158828250)

[Appendix G: Additional Points Of Discussion
75](#__RefHeading___Toc158828251)

[]{#__RefHeading___Toc158828208 .anchor}Table of Figures

[**Figure 3‑1.** Example contact network (from Targeted Social
Distancing Design for Pandemic Influenza, Glass et al, 2006)..
7](#__RefHeading___Toc158827155)

[**Figure 3‑2.** State transitions of natural history of influenza in
our model (from Targeted Social Distancing Design for Pandemic
Influenza, Glass et al., 2006). 9](#__RefHeading___Toc158827156)

[**Figure 3‑3**. Average Infectivity in time.
11](#__RefHeading___Toc158827157)

**Figure 4-1**. Example table and strategy legend 16

[**Figure 4‑2**. Comparison of Infection Attack Rate Tables for combined
containment strategies without (top) and with (bottom) targeted
vaccination of Children and Teens. 35](#__RefHeading___Toc158827158)

[]{#__RefHeading___Toc158828209 .anchor}Table of Tables

[**Table 3‑1.** Containment Strategies 13](#__RefHeading___Toc158827488)

[**Table 4‑1.** Base Containment Strategy Combination Matrix Infection
Attack Rates, Regionally Mitigated, 90% Compliance..
18](#__RefHeading___Toc158827489)

[**Table 4‑2.** Base Containment Strategy Combination Matrix Infection
Attack Rates, Regionally Mitigated, 60% Compliance.
20](#__RefHeading___Toc158827490)

[**Table 4‑3.** Base Containment Strategy Combination Matrix Infection
Attack Rates, Regionally Unmitigated, 90% compliance.
22](#__RefHeading___Toc158827491)

[**Table 4‑4.** Base Containment Strategy Combination Matrix Infection
Attack Rates, Regionally Unmitigated, 60% Compliance.
23](#__RefHeading___Toc158827492)

[**Table 4‑5.** Longini-like Infection Attack Rates, Regionally
Mitigated, 90% compliance. For Longini-like disease manifestation,
implementation threshold 10 diagnosed. 26](#__RefHeading___Toc158827493)

[**Table 4‑6.** Longini-like Infection Attack Rates, Regionally
Mitigated, 60% compliance. For Longini-like disease manifestation,
implementation threshold 10 diagnosed. 27](#__RefHeading___Toc158827494)

[**Table 4‑7.** Longini-like Infection Attack Rates, Regionally
Unmitigated, 90% compliance. Longini-like disease manifestation,
implementation threshold 10 diagnosed. 28](#__RefHeading___Toc158827495)

[**Table 4‑8.** Longini-like Infection Attack Rates, Regionally
Unmitigated, 90% compliance. Longini-like disease manifestation,
implementation threshold 10 diagnosed. 29](#__RefHeading___Toc158827496)

[**Table 4‑9.** Implementation Threshold 100 Diagnosed Infection Attack
Rates, Regionally Mitigated, 90% compliance..
31](#__RefHeading___Toc158827497)

[**Table 4‑10.** Implementation Threshold 100 Diagnosed Infection Attack
Rates, Regionally Mitigated, 60% compliance..
32](#__RefHeading___Toc158827498)

[**Table 4‑11.** Implementation Threshold 100 Diagnosed Infection Attack
Rates, Regionally Unmitigated, 90% compliance..
33](#__RefHeading___Toc158827499)

[**Table 4‑12.** Implementation Threshold 100 Diagnosed Infection Attack
Rates, Regionally Unmitigated, 60% compliance..
34](#__RefHeading___Toc158827500)

[**Table 4‑13.** Children and Teenager Targeted Pre-Pandemic Vaccination
Infection Attack Rates, Regionally Mitigated, 90% compliance..
36](#__RefHeading___Toc158827501)

[**Table 4‑14.** Children and Teenager Targeted Pre-Pandemic Vaccination
Infection Attack Rates, Regionally Mitigated, 60% compliance.
37](#__RefHeading___Toc158827502)

[**Table 4‑15.** Children and Teenager Targeted Pre-Pandemic Vaccination
Infection Attack Rates, Regionally Unmitigated, 90% compliance..
38](#__RefHeading___Toc158827503)

[**Table 4‑16.** Children and Teenager Targeted Pre-Pandemic Vaccination
Infection Attack Rates, Regionally Unmitigated, 60% compliance..
39](#__RefHeading___Toc158827504)

[**Table 4‑17.** Uniform Transmission Infection Attack Rates, Regionally
Mitigated, 90% compliance.. 41](#__RefHeading___Toc158827505)

[**Table 4‑18.** Uniform Transmission Infection Attack Rates, Regionally
Mitigated, 60% compliance.. 42](#__RefHeading___Toc158827506)

[**Table 4‑19.** Uniform Transmission Infection Attack Rates, Regionally
Unmitigated, 90% compliance.. 43](#__RefHeading___Toc158827507)

[**Table 4‑20.** Uniform Transmission Infection Attack Rates, Regionally
Unmitigated, 60% compliance.. 44](#__RefHeading___Toc158827508)

[**Table 5‑1.** Base Community Containment Design.
47](#__RefHeading___Toc158827509)

[**Table 5‑2.** Pre-Pandemic Vaccination of General Population.
49](#__RefHeading___Toc158827510)

[**Table 5‑3.** Targeted Pre-Pandemic Vaccination of Adults.
50](#__RefHeading___Toc158827511)

[**Table 5‑4.** Targeted Pre-Pandemic Vaccination of Children and
Teenagers. 51](#__RefHeading___Toc158827512)

[**Table 5‑5.** Robustness: Relaxation of Implementation Threshold to 30
Diagnosed. 53](#__RefHeading___Toc158827513)

[**Table 5‑6**. Robustness: Relaxation of Implementation Threshold to
100 Diagnosed. 54](#__RefHeading___Toc158827514)

[**Table 5‑7.** Robustness: Relaxation of compliance to 60%..
55](#__RefHeading___Toc158827515)

[**Table 5‑8.** Robustness: Regionally Unmitigated Epidemic.
56](#__RefHeading___Toc158827516)

[**Table 5‑9.** Robustness: Longini-like Disease Manifestation.
57](#__RefHeading___Toc158827517)

[**Table 5‑10.** Robustness: Uniform Transmission.
58](#__RefHeading___Toc158827518)

# Introduction

## Programmatic Context 

Performed as part of the "*Joint NISAC-CIPDSS Pandemic Influenza
Analysis Task*" for the US Department of Homeland Security, this work
supports Task 1.1.2 "*Evaluation of the Effects of Uncertainties on
Response Effectiveness and Economic Impacts*" as shown below.

> Initial evaluation of the effects of uncertainties about pandemic
> influenza disease characteristics on response effectiveness and costs,
> particularly those uncertainties that can not be resolved until the
> virus attains human to human transmission capability. This would
> include an evaluation of the effectiveness of different regional
> mitigation options as well as the impact differential of response
> timing and mitigation actions. This task is designed to characterize
> the effectiveness of selected response options in the context of
> behavioral responses and enhance the understanding of the economic
> impact of the pandemic.
>
> Disease modeling and analysis personnel will work with CDC and HHS
> experts to refine disease parameter estimates including uncertainties
> and identify selected mitigation strategies for minimizing impacts in
> the United States, assuming that initial efforts to contain the
> disease have failed.

More specifically, this study supports Subtask 2 "*Response
Effectiveness and targeted epidemiological uncertainty analysis.*
*(Principal: NISAC)"* defined as shown below.

> This subtask will utilize the full suite of cross-calibrated epidemic
> modeling capabilities (including EpiSimS, EpiCast, EpiC, Loki-Infect,
> and several EpiScope tools), focusing on issues identified in
> subtask 1. The analysis will address uncertainties in characterization
> and parameterization of the disease manifestations, systematic
> variation of parametric assumptions underlying social networks, levels
> of sympathetic or fear-based isolation, and the ability of the health
> care system to cope with pandemic. Mitigation strategies will include
> various forms and timing of antiviral, vaccine, isolation, closure and
> other behavior modifications, individually and in composition,
> including levels of compliance and strategy implementation thresholds.
> This study should identify those strategies or combinations of
> strategies that are both effective and robust to uncertainties in the
> impending pandemic.

## Accomplishments

In support of specified tasks, the NISAC Advanced Modeling Techniques
Investigation (AMTI) group has:

1.  Continued work with the White House Homeland Security Council's
    Pandemic Implementation Plan (WHHSC PIP) writing team to support the
    design of combined mitigation strategy community containment for
    pandemic influenza using results of the NISAC-AMTI Loki-Infect
    model, a networked agent based model developed to analyze complex
    adaptive systems.

2.  Opened interactions with the NIH funded MIDAS consortium of epidemic
    modelers including Neil Ferguson (Imperial College) and Ira Longini
    (University of Washington).

3.  Refined Loki-Infect to represent the influenza manifestations of
    both Ferguson and Longini as used in MIDAS/NIH models as these are
    the most accepted manifestations of influenza in the literature.

4.  Compared Loki-Infect results, to the extent possible, to past
    epidemics of 1918, 1957 and 1968.

5.  Evaluated the robustness of social distancing strategies to
    increased disease infectivity and transmission networks that are
    less focused on the young (i.e., removal of enhanced relative
    infectivity and susceptibility for children and teenagers, increase
    in number of contacts for adults within the workplace to put them on
    par with children and teenagers in schools).

6.  Completed peer review of "Design of targeted social distancing
    strategies for pandemic influenza" for expedited publication in
    CDC's Journal of Emerging Infectious Disease (Glass et al., 2006).
    This paper, included in [**Appendix
    A**](../AppendixA-EID-06-0255.pdf), contains a description of
    Loki-Infect, a subset of the results from analysis in Glass et al
    (2005b), our comparison to past epidemics (Number 4, above), and our
    evaluation of robustness (Number 5, above).

7.  Worked with medical and public health experts within the WHHSC PIP
    writing team (Richard Hatchett of NIH/NIAID and Carter Mecher of the
    VA) to define an extended set of community containment strategies
    around the concept of Targeted Layered Containment (TLC) that
    included both network based strategies (social distancing) and case
    based strategies (home quarantine and three levels of antiviral
    administration: treatment, home prophylaxis, extended network
    prophylaxis).

8.  Worked with public health expert Vicky Davey of the VA to define
    regionally mitigated and unmitigated implementations of external
    interaction within Loki-Infect and to formulate effective criteria
    for rescinding mitigation strategies that minimize illness, epidemic
    re-occurrence, and social disruption.

9.  Defined an extended simulation matrix required for evaluation of
    network based and case based community containment combination
    strategy efficacy in context of regionally mitigated and unmitigated
    scenarios as a function of critical system parameters and their
    uncertainties (several million simulations).

10. Refined the Loki-Infect simulation environment to accommodate the
    large number of simulations required and make use of Sandia's high
    performance Thunderbird computing cluster (8960 64-bit processors
    each with 6GB RAM), databases for effective organization and query
    of output, and archival systems for reproducibility and quality
    assurance.

11. Worked with scientists at NIH/NIAID (Hillery Harvey, Rob Taylor and
    Lone Simonsen) in the 2006 Discovery Channel Young Scientist
    Challenge on the Avian Influenza Challenge (a nationwide middle
    school science contest) that used preliminary Loki-Infect simulation
    results to weigh the impact of disease against social costs of
    mitigation strategies within communities.

12. Presented initial results of extended simulation matrix (defined in
    Number 9, above) at the National Academies\' Institute of Medicine
    review of Community Containment Strategies for Pandemic Influenza
    held October 25-26, 2006. This presentation is included in
    [**Appendix F**](../AppendixF-RJG-Loki-Infect-IOM.pdf).

13. Completed simulation matrix (defined in Number 9, above) and
    analyzed results as a base evaluation of community containment
    strategy efficacy and robustness to principle uncertainties.

## This Report

This report documents the design (**Section 2.0**), methods (**Section
3.0**) and results (**Section 4.0**) for our base evaluation of
community containment strategy efficacy and robustness. (accomplishment
13 above). In **Section 5.0** we use our results to demonstrate a design
process for effective, robust community containment of pandemic
influenza in light of current uncertainties. We end in **Section 6.0**
with a discussion of three areas in which recommendations for policy can
be made: 1) requirements for robust, effective community containment, 2)
necessity of uniform national policy, and 3) administration of
pre-pandemic vaccine. Summary recommendations are also made for the
continued evaluation and reduction of uncertainty.

# Study Definition

In fall of 2005, Loki-Infect was applied to evaluate the effectiveness
of a range of social distancing and vaccination strategies to mitigate
the spread of pandemic influenza. Through interactions with the WHHSC
PIP writing group over the winter and spring of 2006, Loki-infect
results aided in the design of a combined Targeted Layered Containment
or "TLC" mitigation strategy that forms the basis of a proposed response
to pandemic influenza within the United States (Cetron, 2006; Venkayya,
2006). We note that the CDC has integrated TLC into their Interim
Pre-pandemic Planning Guidance released on February 1, 2007 (CDC, 2007).

To evaluate the likely effectiveness of the TLC mitigation strategy, the
WHHSC PIP group defined a series of large scale epidemiological
simulations, outlining the interventions/parameters, their
compliance/efficacy, outcomes of interest, and a set of simulations to
be conducted ([**Appendix
B**](../AppendixB-Simulations%20to%20test%20proposed%20community%20template%20v8.pdf)).
Each set of simulations were to be conducted at a range of infectivity
yielding overall values of *R~o~* of 1.9, 2.4, and 3.0. Note that *R~o~*
of 1.9-2.0 is the current accepted infectivity range for the 1918
Spanish Flu Pandemic, while a value of 1.6 would be representative of
the 1958 Asian Influenza Pandemic. *R~o~* values of 2.4 and 3.0 are far
above these historic values and thus represent an extremely virulent
influenza strain.

We used the interactions with the WHHSC PIP writing group and their
simulation outline to define our study focused on the evaluation of
community containment strategy robustness in the context of uncertainty.
As a base simulation matrix, we considered:

1)  1 natural history disease manifestation: Ferguson-like reflective of
    that in Ferguson et al. (Ferguson et al., 2006; Ferguson et al.,
    2005);

2)  7 disease infectivity factors (0.75, 1.0, 1.25, 1.5, 2.0, 2.5 and
    3.0) about a base case (yielding an infection attack rate of 50%);

3)  2 boundary conditions for external contact (surrounding communities
    either implementing identical strategies or doing nothing to abate
    the epidemic);

4)  8 community containment strategies applied individually or in
    combination (64 combinations);

5)  1 diagnosis rate (80% of symptomatic);

6)  2 compliance rates (60%, 90%) applied to all social distancing,
    antiviral treatment and antiviral prophylaxis;

7)  1 implementation threshold (day after 10 diagnosed within the
    community);

8)  1 pre-pandemic vaccination strategy (none).

For each set of parameters (disease model, infectivity, infectious
contact network, community containment strategy combination), 100
simulations were conducted over which summary statistics are calculated
(total of 1x7x2x64x1x2x1x1x100 = 179,200 runs).

We then extended our analysis to consider uncertainty in the disease
manifestation through implementation of a substantially different,
though accepted, manifestation with the full set of 2 through 8 above:

9)  Natural history disease manifestation: Longini-like reflective of
    that in Longini et al. (Germann et al., 2006; Longini et al., 2005).

After evaluation of the difference between disease manifestations with
this set, we then worked with the Ferguson-like manifestation alone and
extended the matrix in bullets 7 and 8 above to consider additional
uncertainties:

10) Relaxed implementation thresholds for mitigation activity (day after
    30 or 100 diagnosed within the community);

11) 3 pre-pandemic vaccination strategies with 7% coverage of 50%
    efficacy vaccine administered: randomly targeted to children and
    teens or targeted to adults. This constitutes the proposed level for
    a pre-pandemic vaccine stockpile.

Finally, we conducted a first level evaluation of uncertaintly in the
social network using the Ferguson-like manifestation and the original
set of values for bullets 2 through 8 above:

12) Uniform transmission within populations of children, teens, and
    adults (uniform relative infectivity and susceptibility, and
    identical number of contacts within workplaces and schools).

This final evaluation considered a network absent of enhanced
transmission by the young, i.e., the enhanced relative infectivity and
susceptibility for children and teenagers was removed and the number of
contacts for adults within the workplace was increased to put them on
par with children and teenagers in schools. While we believe these two
characteristics are unlikely (especially in combination), they represent
an extreme that we believe will bound our uncertainty in the resulting
network of infectious contacts.

# Methods

## Loki-Infect Model

Loki is a generalized networked-agent modeling toolkit that has been
developed by the National Infrastructure Simulation and Analysis Center
to model critical infrastructures and their interdependencies (Glass,
2005). Agent-based models treat entities (individuals, groups)
explicitly as *agents*. Individual agents are endowed with behavioral
rules for internal states and interaction with other agents or the
external environment. Such models have been developed and applied in a
wide range of fields including economics (Feigenbaum, 2003), sociology
(Goldstone and Janssen, 2005), and more recently epidemiology (Eubank et
al., 2004). Within the epidemiological context, a number of theoretical
studies show the critical importance of the underlying contact network
along which an infectious disease spreads (Barthelemy et al., 2005;
Newman, 2002). The Loki simulation approach combines both agents and
explicit networks (Glass, 2005).

Loki has been applied to: generic congestive cascade (LaViolette et al.,
2006), power grids (Glass et al., 2005a), payment systems (Beyeler et
al., 2006; Glass et al., 2005a; Soramaki et al., 2006), social
simulation (Backus and Glass, 2005), and infectious diseases (Glass et
al., 2005b; Glass et al., 2006).

Loki-Infect is our infectious disease application in which agents
represent individual people and are linked to each other within and
among groups to form a contact network reflective of a
multiply-overlapping, structured community. Behavioral rules for agents,
their interaction, and the performance of network links, have been
specified to model the spread of influenza. Community containment
strategies are implemented through modifications of these behavioral
rules. A copy of our recent paper documenting Loki-Infect and its
application to the design of targeted social distancing (Glass et al.,
2006) is included in [**Appendix A**](../AppendixA-EID-06-0255.pdf).

### Contact Network 

A social contact network is created by first specifying groups of given
sizes (or range of sizes) within which individuals of specified ages
interact (e.g., school classes, households, bridge clubs). The average
number of individuals with which a person has contact within the group
is also specified to reflect that within any group, cliques form or are
imposed (e.g., seating in a class room). This average number is used to
construct a within-group network which can take a variety of forms. For
the stylized community simulated here, we use either fully connected,
random, or ring networks for each group. Random networks are formed by
choosing two individuals at random within the group and linking them.
This connection process is repeated until the number of links within the
group yields the specified average (each individual will have a
different number of links). The ring is formed by first placing each
individual next to a neighbor and linking them to form a complete
circle. Additional links are then made to next nearest neighbors, etc.,
symmetrically around the ring (see Figure 3-1). Finally, links within a
group are given an average frequency of contact (contacts per day). With
this approach, a contact network can be built straightforwardly from the
experience of community members that exhibits the clustered yet
"small-world" character (Watts and Strogatz, 1998) and the
multiply-overlapping quality of a structured community (Newman and Park,
2003; Palla et al., 2005).

![](media/image5.wmf){width="4.559722222222222in"
height="4.502083333333333in"}

[]{#__RefHeading___Toc158827155 .anchor}**Figure 3‑1. Example contact
network (from Targeted Social Distancing Design for Pandemic Influenza,
Glass et al, 2006).** Groups and typical person-to-person links for a
model teenager. The teenager (T1) belongs to a household (fully
connected network, mean link contact frequency 6/day), an extended
family or neighborhood (fully connected network, mean link contact
frequency 1/day), and 6 school classes (ring network with connections to
2 other teenagers on each side as shown in black; purple links denote
connections of other teenagers within the class; mean link contact
frequency 1/day). Two random networks are also imposed, 1 within the age
group (teenager random, average of 3 links/teenager, mean link contact
frequency of 1/day), and 1 across all age groups (overall random,
average of 25 links/person \[not all links shown\], mean link contact
frequency of 0.04/day).

For our current analysis, we constructed our contact network to
represent a stylized small town within the United States. The population
of 10,000 conforms to the 2000 Census (2000) and consists of children
(0-11 years of age, 17.7%), teenagers (12-18 years of age, 11.3%),
adults (19-64 years of age, 58.5%) and seniors (65+ years of age,
12.5%). All individuals belong to multiple groups, each associated with
a sub-network of links reflecting their lives within the community. A
typical teenager's groups and contact network is shown in Error:
Reference source not found. Complete group specifications are reported
in **Table 1** of Glass et al, 2006 in [**Appendix
A**](../AppendixA-EID-06-0255.pdf). Households are composed of families
(adults with children/teenagers) or adults and/or seniors without
children/teenagers. The age class makeup and size of households was
chosen to conform to the statistics of the 2000 Census (2000). All
individuals within each household are linked to each other (fully
connected sub-network topology) with mean link contact frequencies of 6
contacts/day. Every individual also belongs to one multi-age extended
family (or neighborhood) group that has a mean membership of 12.5 and is
fully connected with mean link contact frequencies of 1 contact/day.

All children and teenagers go to a pre-school or school; children attend
a single class per day while teenagers attend six (all classes of size
20-35). All adults go to work daily where they interact with other
adults (size 10 to 50), and all seniors attend senior gatherings (size 5
to 20). For contacts within school classes, work, and senior gatherings,
we assume the simplest sub-network topology that imposes local
clustering: a ring lattice in which an individual is linked to two (for
children/teenager classes and senior gatherings) or three (adult work)
neighboring individuals on each side along the ring (see Error:
Reference source not found). Mean link contact frequencies for children
in a single class are 6 contacts/day while teen classes, adult work, and
senior gatherings have mean link contact frequencies of 1 contact/day.

To represent additional within-age-class interactions such as
extracurricular activities, playgrounds, bowling leagues, or friends,
individuals are linked at random to an average of three other
individuals of the same age class (mean link contact frequency of 1
contact/day). Finally, to emulate a somewhat patterned set of random
contacts that come from commercial transactions and other ventures into
public spaces, we impose a random over-all network across all age
classes with a mean of 25 links per person to yield one contact per
person per day (mean link contact frequency of 0.04/day).

### Behavioral Rules 

The spread of influenza within the contact network is modeled as a
series of events. There are 2 classes of events: the transition of a
person between disease states and person-to-person influenza
transmissions. State transitions follow the natural history of influenza
(see ).

![](media/image6.wmf){width="6.122916666666667in"
height="3.015277777777778in"}[]{#__RefHeading___Toc158827156 .anchor}

**Figure 3‑2. State transitions of natural history of influenza in our
model (from Targeted Social Distancing Design for Pandemic Influenza,
Glass et al., 2006).** Duration of each state for a given person is
chosen from an exponential distribution. State relative infectivity
(*I~R~*) and mean state duration were chosen to reflect the infectivity
variation of normal influenza (see **Figure 3-3**) and those shown in
the figure are for the Ferguson-like disease manifestation.

After the latent state, an infected person transitions to a
presymptomatic infectious state or an infectious asymptomatic state with
probability *pS* or *1 -- pS*, respectively. Those in whom symptoms
develop either stay home with probability *pH*, thus influencing their
contacts, or continue to circulate with probability *1 -- pH*. Infected
persons who are asymptomatic continue interacting without behavioral
changes. Persons who are symptomatic transition to dead or immune with
probability *pM* or *1 -- pM*, respectively, and asymptomatic persons
simply transition to immune. Finally, we append a recovery period for
every individual who becomes symptomatic but does not die.

Person-to-person transmission events are evaluated at the beginning of
each period during which a person is infectious. Assuming contact events
are statistically independent, a transmission time for each of an
infectious person's links within the contact network is chosen from an
exponential distribution with a mean given by the reciprocal of the
link's contact frequency scaled by *I~D~I~R~I~A~S~P~S~A~* where *I~D~*
is the infectivity of the disease, *I~R~* is the relative infectivity of
the disease state, *S~P~* is the susceptibility of people to the disease
(here taken as 1.0), *I~A~* is the relative infectivity of the person
who is transmitting, and *S~A~* is the relative susceptibility of the
person receiving. If the transmission time is less than the period of
time that the person will be in a particular infectious state (also
chosen from an exponential distribution with prescribed means),
transmission is scheduled at the chosen time. Otherwise, transmission
along that link does not occur during that particular period.

All transmission parameters and contact frequencies may be modified in
each of the various states as well as varied among age classes by using
relative scaling factors such as *I~R~*. In this way, specific disease
manifestations and community containment strategies are implemented.

## Specific Manifestations of Influenza

We consider two manifestations of influenza, one of which conforms
closely to Ferguson et al (Ferguson et al., 2006; Ferguson et al., 2005)
and the other to Longini and colleagues (Germann et al., 2006; Longini
et al., 2005).

Ferguson (Ferguson et al., 2006; Ferguson et al., 2005) uses a
functional form for infectivity that matches latent period data (Moser
et al 1979) and viral shedding data (Hayden et al., 1998). While he uses
this for individuals, we match this functional form at the population
scale (averaged across the population). This is represented in
Loki-Infect with the following state periods and relative infectivities:

-   latent offset (constant 0.75 days),

-   latent (mean of 0.5 days),

-   infectious pre-symptomatic (mean of 0.5 days, relative infectivity
    0.25),

-   infectious symptomatic1 (mean of 0.5 days, relative infectivity
    1.0),

-   infectious symptomatic2 (mean of 1.0 days, relative infectivity
    0.35).

Half of infected become symptomatic (*pS* = 0.5), infectious
non-symptomatic have half the infectivity of symptomatic.
Non-symptomatic infectivity is represented in Loki-Infect with a
constant relative infectivity 0.25 for mean of 2 days starting after the
latent period.

Longini's disease manifestation (Germann et al., 2006; Longini et al.,
2005) is represented in Loki-Infect with the following states and
relative infectivities:

-   latent offset 0.75 days,

-   latent (mean of 0.45 days),

-   pre-symptomatic (mean of 0.7 days, relative infectivity 1.0),

-   symptomatic1 (mean of 3.4 days, relative infectivity 1.0).

Two thirds of infected develop symptoms (*pS* = 0.67), infectious
non-symptomatic have half the infectivity of symptomatic (mean duration
4.1 days, relative infectivity 0.5).

Common to both manifestations and in conformance with the WHHSC PIP
group simulation outline (see [**Appendix
B**](../AppendixB-Simulations%20to%20test%20proposed%20community%20template%20v8.pdf))
we have taken:

-   Diagnosis: of infectious symptomatic at 0.8 and all diagnosed go
    home where they remain while sick (*pH* = 0.8, this is age class
    independent), all non-household contacts reduced by a compliance
    factor (60%, 90%), household contacts remain the same. Those that
    are not diagnosed continue to circulate, no distinction by age
    class.

-   Babysitting: one household adult stays home with a diagnosed child
    (11 or younger) while they are sick at home or with the child when
    schools are closed. In this state, all non-household contacts for
    the babysitter are reduced by a compliance factor (60%, 90%),
    household contacts for babysitter are doubled when tending well
    children (just as for the rest of the household members when schools
    are closed) but not doubled for tending sick children.

-   Mortality: *pM* = 0.02, no distinction by age class.

-   Recovery: a final recovery period with mean of 7 days

The infectivity averaged over the population of those who are infected
within a typical simulation for both disease manifestations at an
infection attack rate of \~50% is shown in **Figure 3-3**. The viral
shedding data of Hayden et al. (Hayden et al., 1998) is also plotted for
comparison. These data are scaled to fit the maximum value of each
disease manifestation and comparison shows reasonable functional
correspondence with average population scale results for Ferguson-like
but not Longini-like disease manifestations. Thus the Longini-like
manifestation represents a virus with a lower but longer acting
infectivity.

[]{#__RefHeading___Toc158827157 .anchor}Figure
3‑3![](media/image7.jpeg){width="4.833333333333333in"
height="3.691666666666667in"}. Average Infectivity in time. Average
population scale *I~R~* in time for Ferguson-like and Longini-like
disease manifestations. Viral shedding data from Hayden (Hayden et al.,
1998) scaled to the peak for each disease manifestation is shown for
comparison.

## Network of Infectious Contacts

For a given disease manifestation (Ferguson-like or Longini-like) and
disease infectivity (*I~D~*), the network of infectious contacts is
dependent on both the contact network and the choice of age class
specific infectivity and susceptibility (*I~A~* and *S~A~*). As a base
case, *I~A~* and *S~A~* were considered to have equal values within each
age class with: children 1.5, teenagers 1.25, adults and seniors 1.0.
This assumes that children and teenagers individually are more infective
and susceptible, as they have closer contact with others (hugging,
wrestling, holding hands, etc.) and are less likely to wash hands or
control coughing (Cauchemez et al., 2004). As shown in Targeted Social
Distancing Design for Pandemic Influenza (Glass et al, 2006), this base
case emphasizes transmission among the young and yields age class
specific attack rates within our community reflective of past epidemics
(see **Figure 6** in [**Appendix A**](../AppendixA-EID-06-0255.pdf)).

The strain of influenza that emerges in the next pandemic may not hit
children and teenagers harder than adults and seniors. Additionally, the
social contact network may have more emphasis on adults within the
working environment than currently considered. Both of these
possibilities reduce the transmission within children and teenagers
relative to transmission within the adult population and change the
resulting network of infectious contacts. To address this potential, an
extension to our base simulation matrix was developed in which the
enhanced relative infectivity and susceptibility for children and
teenagers are removed entirely and the number of contacts for adults
within the workplace are increased by a factor of 4 to put them on par
with children and teenagers in schools. While we believe these two
characteristics to be unlikely, especially in combinations, they
represent an extreme that likely bounds our uncertainty in the resulting
network of infectious contacts.

## Choosing Disease Infectivity *I~D~*

Following selection of values for contact network parameters, disease
manifestation, and relative infectivity for various age classes, the
overall infectivity of the disease (*I~D~*) is the final parameter used
to tune the simulations to yield attack rates with different basic
reproductive numbers (*R~o~*) for an epidemic. For our systematic
variation of disease infectivity, we first find a reference *I~D~* that
yields \~50% infection attack rate (25% illness attack rate for
Ferguson-like, 33% illness attack rate for Longini-like disease
manifestations) reflective of the 1958 pandemic (where the best data for
age class attack rates exits). *I~D~* was then scaled by factors of
0.75, 1.0, 1.25, 1.5, 2.0, 2.5 and 3.0 to yield both lower and higher
attack rates. We refer to this scaling factor as the IDfactor in the
remainder of this report. An IDfactor of 1.5 is reflective of the 1918
pandemic. *I~D~* for the reference 50% infection attack rate is chosen
independently for each set of contact network parameters, disease
manifestation and compliance level (compliance influences sick at home
and babysitting behavior and thus the attack rate) so that comparisons
of strategy efficacy may be made evenly across the full set of
combinations.

## Instigation and Boundary Conditions

For the base matrix of community containment strategy combinations, each
simulation is instigated with 10 adults chosen at random (the business
traveler assumption). Alone, this models a closed community with no
further interaction outside. It also models a fully open community in
interaction with like communities implementing identical mitigation
strategies and similarly seeded.

As a possible worst case and along the lines of recent work by Davey and
Glass (Davey and Glass, 2007), we also consider our community as
surrounded by a regional population within which no mitigation
strategies are implemented. Contact with this regional population is
conceived of as exclusively through the work environment. There, it is
assumed that contacts along all work links are replaced with random
contacts with a fully mixed reservoir of external adults. The fraction
of those adults that are contagious as a function of time is modeled by
the baseline epidemic for the given IDfactor and compliance. Thus the
regional population is assumed to be uninfluenced by the course of the
disease within the local community. Preserving the number of contacts
within the work environment, the fraction that contact a contagious
external adult (given by their fully mixed contagious fraction) are
infectious with probability *I~D~\<I~R~\>I~A~S~A~F*. *\<I~R~\>* is the
weighted average over symptomatic (reduced by diagnosis) and
asymptomatic individuals for the mean contagious period and *F* is the
current work frequency scaling for the particular adult agent chosen at
random from the community\'s population. *F* reflects the current
situation of the adult such as sick at home or babysitting and the
particular strategy implemented (quarantine or social distancing) all
modified by compliance. The relative susceptibility for the person
(*S~A~*) is adjusted if the adult is receiving antiviral prophylaxis.
The restriction of external contact to within the normal work
environment seems reasonable during a period of pandemic. This approach
also simulates an embedded geographically contiguous local sub-community
within a larger city where contacts outside the household are mainly
within the local community except at work where none may be so.

## Community Containment Strategies 

From the WHHSC PIP writing group simulation outline (see [**Appendix
B**](../AppendixB-Simulations%20to%20test%20proposed%20community%20template%20v8.pdf)),
we distilled 8 independent containment strategies (S, CTsd, ASsd, Q, T,
P, and Pex) defined below. Each strategy can have varying compliances
and thresholds for implementation yielding an infinite set of
combinations. In conformance with the WHHSC outline, we applied two
levels of implementation (compliance) as good (60%) and very good (90%),
and one threshold for strategy implementation (following the diagnosis
of 10 symptomatic individuals within the community). Relaxations of the
implementation threshold (following either 30 or 100 diagnosed
individuals) were analyzed as an extension to our base simulation
matrix.

[]{#__RefHeading___Toc158827488 .anchor}Table 3‑1. Containment
Strategies

  ---------- --------------------------------------------------------------
  **S**      Schools closed, all school contacts reduced by 90%, household
             contacts doubled

  **CTsd**   Children&teenagers social distancing, all non-school and
             non-household contacts with or between children and teenagers
             reduced by (60%, 90%), household contacts doubled

  **ASsd**   Adults&Senior social distancing, all non-household, non-work
             contacts within and between adults and seniors reduced by
             (60%, 90%), work contacts reduced by 50%, household contacts
             doubled

  **Q**      Household Quarantine for 10 days once an individual is
             diagnosed, all non-household contacts reduced by (60%, 90%),
             household contacts doubled

  **T**      Antiviral Treatment, individual given antiviral course with
             probability (60%, 90%) for 5 days immediately after diagnosed,
             reduces infectivity by 60% from that point forward (Ferguson
             et al., 2006; Ferguson et al., 2005)

  **P**      Antiviral Prophylaxis, household members given antiviral with
             probability (60%, 90%) for 10 days starting immediately after
             reference case diagnosed, reduces susceptibility by 30%,
             reduces probability of symptomatic by 65%, reduces infectivity
             by 60% (Ferguson et al., 2006; Ferguson et al., 2005)

  **PEx**    Extended Antiviral Prophylaxis, household members, workplace
             contacts, school contacts, work contacts and
             neighborhood/extended family contacts given antiviral with
             probability (60%, 90%) for 10 days starting immediately after
             reference case diagnosed, reduces susceptibility by 30%,
             reduces probability of symptomatic by 65%, reduces infectivity
             by 60%. (Note that school and workplace contact rates used
             here are much less than the entire school or work groups.
             Ferguson's implementation: children's groups 90%, teenager's
             groups 90%, adult's groups 90%. Longini's implementation:
             children's groups 100%, teenager's groups 60/80%, adult's
             groups 60/80%)
  ---------- --------------------------------------------------------------

For a given compliance level, each strategy is implemented separately or
in combination to yield a full matrix of combinations for evaluation.
Antiviral strategies T, P and Pex are nested, with P necessarily
incorporating T, and Pex necessarily incorporating both T and P. Thus, a
matrix of 64 combinations of containment strategies is constructed and
used as a base simulation matrix as other parameters (disease
manifestation, implementation threshold, boundary condition, compliance
and infectivity) are varied.

A recent condition study Davey and Glass (Davey and Glass, 2007) that
ceasing mitigation strategies following 7 days with no newly diagnosed
individuals (corresponding to 2 to 3 generation periods depending on the
disease manifestation, see [**Appendix C**](#OLE_LINK2)) was
sufficiently effective to contain an epidemic. Subsequently, if the
number of newly diagnosed individuals rises above the implementation
threshold (10, 30 or 100), containment strategies are reapplied and a
second containment cycle begins. If required, additional cycles based on
these beginning and ending conditions may be implemented until no
infected individuals remain within the community.

As extensions to our base containment strategy combination matrix, three
pre-pandemic vaccination strategies were also analyzed based on 7%
coverage of a 50% effective vaccine administered 1) randomly, 2)
targeted to children and teens, or 3) targeted to adults. For each of
these target groups, the vaccine was administered before the initial
seeding of infected adults. The full simulation matrix (64 containment
strategy combinations, 7 IDfactors, 2 compliances, and 2 boundary
conditions) was then conducted.

# Results

In addition to documenting the complete sequence of infectious contacts
that take place, each simulation yields overall and daily output for a
variety of measures. All output is automatically written into databases
that can be queried by input or output to yield statistics of interest.
Across all analyses, we have focused on 15 measures:

-   number of simulations that yield epidemics (defined as \> 1% of
    population infected)

-   infection attack rate

-   illness attack rate

-   deaths

-   peak infected

-   time to peak infected

-   peak symptomatic

-   time to peak symptomatic

-   epidemic duration (from first 10 diagnosed to last diagnosed)

-   total time of effects (from initial seeding to last person
    recovered)

-   number of days strategies imposed

-   number of containment cycles

-   number of external infections

-   number of antiviral courses given

-   number of days adults are at home (either sick, quarantined, or
    tending sick or sent home from school children)

For these measures, we find means and standard deviations across each
set of 100 runs for a given containment strategy combination,
infectivity, compliance, and boundary condition. These analyses are
grouped by disease manifestation, vaccination strategy, implementation
threshold and infectious contact network. Only those simulations that
created epidemics (defined as \> 1% of the population infected) are used
in calculating statistics.

Full results are compiled within excel work sheets presented in the
Appendices. Unmitigated base cases are presented and analyzed within
[**Appendix C**](#OLE_LINK2) for both Ferguson-like and Longini-like
disease manifestations. [**Appendix D**](#OLE_LINK3) contains the base
containment combination matrix results for the Ferguson-like disease
manifestation, while the matrix extensions for the Longini-like disease
manifestation, relaxed implementation thresholds, vaccination
strategies, and infectious contact network variations are compiled
within additional excel work sheets in [**Appendix E**](#OLE_LINK1).
Below we summarize our observations on containment strategy efficacy.

## Base Containment Strategy Combination Matrix for Ferguson-like Disease Manifestation

For each of the 15 summary measures, we create a set of 4 tables and
accompanying 3D bar graphs within the Excel worksheets of [**Appendix
D**](#OLE_LINK3). Each of the 4 tables and sets of graphs present
results for 1) 90% compliance, 2) 60% compliance, 3) 90% compliance
where adults are in contact with an external base case epidemic, and 4)
60% compliance where adults in contact with an external base case
epidemic.

![](media/image8.wmf){width="1.554861111111111in"
height="2.0in"}**Figure 4-1**, to aid in viewing this data within the
tables, those combinations that yield an infection attack rate that is
10% or less are shaded green and those between 10% and 25% are shaded
pink. The set of 4 tables for the infection attack rate are shown here
as **Tables 4-1, 4-2, 4-3** and **4-4** to aid our presentation below.

Time series plots for daily measures averaged over the set of 100
simulations may be made for any of the combinations. An example set for
an IDfactor of 1.5 and Ferguson-like disease manifestation that
considers the measures of people infected, treated with antivirals,
adults at home, and symptomatic containment strategies are attached as
pdf files in [**Appendix D**](#OLE_LINK3).

### 90% compliance: 

**Table 4-2** shows the infection attack rate resulting from 90%
compliance where the community is embedded within a region implementing
identical containment strategies. At the lowest IDfactor (0.75), the
efficacy of network focused strategies applied alone increases from
ASsd, CTsd, CTsd+ASsd, S, S+ASsd, A+CTsd, to S+CTsd+ASsd. As the
IDfactor increases, case-based measures that include ASsd increase in
efficacy relative to those with CTsd. This is because the branching
factor for adults is pushed above 1 (see [**Appendix C**](#OLE_LINK2)),
there are more adults in the community, and ASsd includes the work
environment while CTsd does not include schools. Applied alone, the
efficacy of case-based strategies increases from T, Q, P, Q+T, Q+P, Pex,
to Q+Pex. This order does not change as the IDfactor increases.

Network based strategies can more effectively drop the infection attack
rate than case-based strategies. For influenza virulence above an
IDfactor of 1, case-based strategies alone cannot drop the infection
attack rate below 10%, while network-based strategies can accomplish
this up to an IDfactor of 1.5 when all conditions (S+CTsd+ASsd) are
required,.

Combining network-based and case-based strategies across the 64
combinations yields banded green (where infection attack rates are 10%
or less) and pink (where infection attack rates are 10 to 25%) zones
within each IDfactor region in the tables. The less than 10% green zone
is concentrated in each lower right hand corner where all strategies are
imposed. As can be seen in both the tables and the 3D bar graphs, there
is a sharp falloff in attack rate within the pink 10-25% region. All
time scales (epidemic duration, total time, times to peak) increase
above the base case within the pink region, while once within the green,
they quickly fall below and continue to decrease as one moves to the
lower right hand corner of each IDfactor region.

Strategy combinations that are as far in the less than 10% attack rate
(green) zone as possible are most effective. Not only are fewer local
epidemics triggered with fewer people infected, symptomatic or dead,
epidemics last much less time with greatly suppressed peaks and
ultimately, a much reduced total cost. This is born out in the number of
days that adults are at home: implementing S+CTsd+ASsd always decreases
this number over S+CTsd alone. Of course, implementing S is the major
component of this measure because closing the schools requires \~1300
adults to be sequestered at home to mind children. We note that this is
a worst case assessment because we assume that all adults go to work and
it is likely that many of the child minding adults could maintain
reasonable work productivity (telecommuting, time shifting, job
sharing). Additionally, teenagers present within the household could
provide the oversight of children and thus release the adult babysitter
to go to work.

The measure of days adults are at home needs more discussion. 1) We
assume that all adults participate in a work group. This is not a large
problem as we could easily interpret some of these work groups as non
work activity groups composed of non working adults. To adjust for these
unemployed in the calculation of work force reduction, the number of
adult days at home should be reduced by the fraction of unemployed. 2)
Every day is a work day. To adjust for weekends, two days out of seven
should also be removed from the measure to apply to the number of days
adults are absent from work. 3) ASsd includes a reduction in contact
frequency of 50%. This is assumed to be accomplished within the
workplace without adults staying at home. If this is not true, the
number of days adults would be absent from work should be increased by
the fraction of the time not present (50%) times the average duration of
the ASsd strategy.

The application of a strategy ending threshold of 7 days with no new
diagnosed people works well. The generation period for the Ferguson-like
manifestation is 2.6 days (see [**Appendix C**](#OLE_LINK2)) and so this
period is just short of 3 generation periods. On average, and across all
the IDfactors, additional cycles are needed only 10% of the time and it
is rare that more than one additional cycle must be imposed.

For strategies resulting in attack rates of 10% or less (the green
zone), required antiviral courses are below 40% coverage. Excluding Pex,
a maximum of only 8% coverage is required within this zone, and for most
of the combinations, far less. Applying Pex alone is only effective
(green) below IDfactor of 1 and at higher IDfactors, can lead to a
coverage of almost 150% where each individual receives an antiviral
course an average of 1.5 times over the course of the epidemic. These
greater than 100% coverages are also very ineffective (outside the green
or pink regions). We note that if we had simply given antiviral to
everyone in the community early enough, 100% coverage would likely have
been more effective than the tracing approach of Pex implemented in the
model. The combination of reduced infectivity and reduced susceptibility
assumed for antiviral prophylaxis together yield a factor of 0.28
reduction in infectious contacts and with full compliance could
theoretically stop an epidemic with an IDfactor of 3.0.

[]{#__RefHeading___Toc158827489
.anchor}![](media/image10.wmf){width="5.359842519685039in"
height="8.0in"}![](media/image11.jpeg){width="6.0007874015748035in"
height="0.7200787401574803in"}**Table 4‑2. Base Containment Strategy
Combination Matrix Infection Attack Rates, Regionally Mitigated, 90%
Compliance.** For Ferguson-like disease manifestation and implementation
threshold 10 diagnosed. Case based strategy combinations downward,
network focused strategy combinations across with: green shading,
infection attack rate 10% or less; pink shading, infection attack rate
between 10% and 25%.

### 60% compliance: 

Reducing compliance to 60% reduces the efficacy of both case based and
network based strategies (**Table 4-2**). Infection attack rates have
been increased thus pushing green (less than 10%) and pink (10-25%)
zones within the tables further to the lower right of each IDfactor
region where more strategies must be implemented; regions with attack
rates less than 10% (green) have been entire lost for IDfactors above
1.5, regions with attack rates between 10-25% (pink) have been lost for
IDfactors above 2.0.

Relative rankings within network based strategies have been maintained,
however, for case based strategies, Q has fallen below T, and Q+T has
fallen below P. Additionally, antiviral strategies increase their
relative efficacy to be nearer to network based strategies. Some of this
increase in relative efficacy of antivirals is due to the fact that when
Q or any of the network based strategies are implemented, the contact
frequency within the household is doubled and we maintain this doubling
for both 90% and 60% compliances.

Reducing compliance also increases epidemic time scales but within most
of the green zone (less than 10% attack rate) they remain at or below
that of the base case. Days adults are home also increase (because time
scales increase) and remain within a factor of 3 of the 90% compliance
values within most of the green zone. While the number of containment
cycles is not significantly influenced, the number of antiviral courses
increases up to nearly a factor of 4 within the green zone. Finally we
note that at lower compliance, Pex becomes more effective at reducing
adult days at home.

[]{#__RefHeading___Toc158827490
.anchor}![](media/image12.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7133858267716535in"}Table 4‑3. Base Containment Strategy
Combination Matrix Infection Attack Rates, Regionally Mitigated, 60%
Compliance. For Ferguson-like disease manifestation and implementation
threshold 10 diagnosed. Case based strategy combinations downward,
network focused strategy combinations across with: green shading,
infection attack rate 10 or less; pink shading, infection attack rate
between 10% and 25%.

### External Contacts: 

When communities within the surrounding regions are implementing no or
ineffective containment strategies, full contact of adults across
communities within the work environment leads to a degradation in the
effectiveness of the local community strategy (**Tables 4-3 and 4-4**).
In general, attack rates rise above 10% (green regions in the tables
shrink). At 90% compliance, the efficacy of local containment strategies
shrinks to near that of 60% compliance with a uniform regional policy.

At 60% compliance, continued interaction with contagious adults from
outside reduces local strategy efficacy enough that attack rates of less
than 10% (a green zone) cannot be found at an IDfactor of 1.5, and at an
IDfactor of 1.25, green strategies require Pex with nearly 40% antiviral
coverage. . Within the green zones of the tables, time scales all
approach the base case with a corresponding factor of 2-3 increase from
the regionally mitigated simulations (**Tables 4-1 and 4-2**) in days
adults are at home.

[]{#__RefHeading___Toc158827491
.anchor}![](media/image13.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}Table 4‑4. Base Containment Strategy
Combination Matrix Infection Attack Rates, Regionally Unmitigated, 90%
compliance. For Ferguson-like disease manifestation and implementation
threshold 10 diagnosed. Case based strategy combinations downward,
network focused strategy combinations across with: green shading,
infection attack rate 10 or less; pink shading, infection attack rate
between 10% and 25%.

[]{#__RefHeading___Toc158827492
.anchor}![](media/image14.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑5. Base Containment Strategy
Combination Matrix Infection Attack Rates, Regionally Unmitigated, 60%
Compliance. For Ferguson-like disease manifestation and implementation
threshold 10 diagnosed. Case based strategy combinations downward,
network focused strategy combinations across with: green shading,
infection attack rate 10 or less; pink shading, infection attack rate
between 10% and 25%.

## Base Matrix Extensions

Simulations from the base containment strategy combination matrix were
first extended to analyze the influence of disease manifestation by
running the full matrix for the Longini-like version (see section 3.2
for a comparison of Ferguson-like and Longini-like disease
manifestations). Then, returning to the Ferguson-like manifestation, we
extended the matrix to include: relaxation of implementation threshold
to the day after 30 and 100 are diagnosed within the community; and 3
vaccination strategies with 7% coverage 50% efficacy administered 1)
randomly, 2) targeted to children and teens or 3) targeted to adults.
Finally, we conducted a first level evaluation of the influence of the
social network using the Ferguson-like manifestation, implementation
threshold of 10 symptomatic diagnosed in the community, and no
pre-pandemic vaccination. This evaluation implemented a network absent
of enhanced transmission by the young, i.e., the enhanced relative
infectivity and susceptibility for children and teenagers was removed
and the number of contacts for adults within the workplace was increased
by a factor of 4 to put them on par with children and teenagers in
schools (such was considered as bounding in Glass et al., 2006). For
each of the matrix extensions, we create a set of Excel worksheets
similar to those for the base containment strategy combination matrix
and include them in [**Appendix E**](#OLE_LINK1).

### Longini-like disease manifestation:

Once the disease infectivity (*I~D~*) is tuned to yield an infection
attack rate of \~50% for the unmitigated base case, total and age class
specific infection attack rates for both the Ferguson-like and
Longini-like disease manifestations are indistinguishable across the
full range of IDfactors and for both compliances (well within one
standard deviation (SD) of each other). Maximum branching factors by age
class and overall (an estimate of *R~o~*, see [**Appendix
C**](#OLE_LINK2)) are indistinguishable up to an IDfactor of 3.0 (a
highly infectious and unlikely case) at which point the maximum
branching factor for the Longini manifestation falls below that of
Ferguson by \~10%. Infectious contact fractions by age class and by
transmission context also show no significant difference (nearly all
within one SD of each other).

However, because the time scale of the Longini-like manifestation is
longer, all measures influenced by time scale are stretched. For the
unmitigated epidemic, generation time increases by \~40% (from 2.37 to
3.35 days), epidemic duration by 55%, total time by 20%, time to peak
infected by 36%, time to peak symptomatic by 31%. Peak infected also
increases slightly by 10%. Due to the 33% increase in the probability of
becoming symptomatic when infected (*pS)* within the Longini-like
disease manifestation, the total number of symptomatic is increased
(34%) as well as their peak value (28%). These values for symptomatic
translate directly into a 34% increase in deaths. The combination of the
increase in *pS* and the longer time scales translate into a 61% greater
number of days that adults are at home sick or tending sick children for
the unmitigated base case.

**Tables 4-5, 4-6, 4-7, and 4-8** show the infection attack rate for the
full set of containment strategy combinations, IDfactor, compliance and
connection with external epidemic (full set of tables for this extension
are within [**Appendix E**](#OLE_LINK1)). In the tables, strategy
combinations that meet the infection attack rates of less than or equal
to 10% and between 10 and 25% have been colored green and pink,
respectively, as before.

For social distancing strategy combinations, the infection attack rates
for the Longini-like disease manifestation are nearly identical to the
Ferguson-like, and those strategies within either green or pink zones do
not change. However, for antiviral strategies, the Longini-like
manifestation proves more effective (both green and pink zones
increase). This happens because the increased time scale of the epidemic
allows prophylaxis to better capture the spreading disease (see
[**Appendix G**](#OLE_LINK4)). Over all containment strategy
combinations, the infection attack rate for the Ferguson-like
manifestation is slightly higher, the average difference at 90%
compliance is 1.5% (max 11.6, min -6.9, SD 2.2%). With decreasing
compliance and contact with an external base epidemic, this difference
decreases somewhat (and the range and SD decrease by almost half).

While the illness attack rate for the unmitigated epidemic is 33%
greater for the Longini-like manifestation, the average difference
between Ferguson-like and Longini-like across the four containment
strategy combination tables is insignificant (between -3.9 and -6.3 with
SD of 4.6 across both compliance and connection with external base
epidemic). Most of these differences occur for strategy combinations
that are ineffective. When effective containment strategy combinations
are implemented, the two manifestations produce nearly identical
outcomes (differences in illness attack rate almost all below 1%).

Over all containment strategy combinations, the Longini-like
manifestation requires more anitiviral courses with an average
difference at 90% compliance of -4.9% (max 28.6, min -52.1, SD 12.6).
These average differences do not change significantly with decreasing
compliance and contact with the external base epidemic. Once again,
differences reduce significantly as strategy combinations achieve an
infection attack rate of 10% or less (green zone).

Finally, the average difference between adult days at home at 90%
compliance for Ferguson-like and Longini-like manifestations is -3.6
(max 4.6, min -16.6, SD 3.8). This increase in days adults are home for
the Longini-like manifestation does not change significantly with
decreasing compliance and contact with the external base epidemic.
Unlike for illness attack rate and antiviral courses, these average
differences also do not significantly change as one moves into the green
zone.

[]{#__RefHeading___Toc158827493 .anchor}Table 4‑6. Longini-like
Infection Attack Rates, Regionally Mitigated, 90% compliance. For
Longini-like disease manifestation and implementation threshold 10
diagnosed. Case based strategy combinations downward, network focused
strategy combinations across with: green shading, infection attack rate
10 or less; pink shading, infection attack rate between 10% and 25%.

![](media/image15.wmf){width="5.361023622047244in"
height="8.007086614173229in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}

> []{#__RefHeading___Toc158827494
> .anchor}![](media/image16.wmf){width="5.305511811023622in"
> height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
> height="0.7188976377952756in"}Table 4‑7. Longini-like Infection Attack
> Rates, Regionally Mitigated, 60% compliance. For Longini-like disease
> manifestation and implementation threshold 10 diagnosed. Case based
> strategy combinations downward, network focused strategy combinations
> across with: green shading, infection attack rate 10 or less; pink
> shading, infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827495
.anchor}![](media/image17.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.9374015748031495in"
height="0.7082677165354331in"}Table 4‑8. Longini-like Infection Attack
Rates, Regionally Unmitigated, 90% compliance. For Longini-like disease
manifestation and implementation threshold 10 diagnosed. Case based
strategy combinations downward, network focused strategy combinations
across with: green shading, infection attack rate 10 or less; pink
shading, infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827496
.anchor}![](media/image18.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑9. Longini-like Infection Attack
Rates, Regionally Unmitigated, 90% compliance. For Longini-like disease
manifestation and implementation threshold 10 diagnosed. Case based
strategy combinations downward, network focused strategy combinations
across with: green shading, infection attack rate 10 or less; pink
shading, infection attack rate between 10% and 25%.

### Relaxing Implementation Threshold: 

In Glass et al (Glass et al., 2006) we showed that relaxation of the
implementation threshold with S+CTsd rapidly eroded effectiveness. We
also find this to be the case for our full containment strategy
combination matrix in which the higher the IDfactor, the greater the
erosion. For an implementation threshold of 100 diagnosed individuals,
the Ferguson-like disease manifestation infection attack rates (shown in
**Tables 4-9, 4-10, 4-11, and 4-12)** reflect significantly fewer
mitigation strategies available to keep infection attack rates below 25%
(green and pink zones). A full set of tables for this extension can be
found in [**Appendix E**](#OLE_LINK1). Because Treatment with antivirals
is not controlled by an implementation threshold, those strategy
combinations that include treatment (T, P and Pex) all erode less than
those that do not.

Within the less than 10% infection attack rate zone (green), the average
time for strategy implementation is delayed by 6 (30 diagnosed) and 14
days (100 diagnosed) at an IDfactor of 1. For an IDfactor of 1.5,
strategies are only able to achieve an infection attack rate of between
10 and 25% (pink zone) and implementation is delayed by 4 (30 diagnosed)
to 7 days (100 diagnosed). These delays translate into similar delay
periods for peak infected and symptomatic. Adult days at home generally
decrease slightly (by about a day) within the green zones as fewer days
are spent minding children sent home from school. However, required
antiviral courses significantly increase for both of the lower infection
attack rate zones (green and pink), the more so as the IDfactor
increases.

[]{#__RefHeading___Toc158827497 .anchor}Table 4‑10. Implementation
Threshold 100 Diagnosed Infection Attack Rates, Regionally Mitigated,
90% compliance. For Ferguson-like disease manifestation. Case based
strategy combinations downward, network focused strategy combinations
across with: green shading,
![](media/image19.wmf){width="5.361023622047244in"
height="8.007086614173229in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}infection attack rate 10 or less; pink
shading, infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827498
.anchor}![](media/image20.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑11. Implementation Threshold 100
Diagnosed Infection Attack Rates, Regionally Mitigated, 60% compliance.
For Ferguson-like disease manifestation. Case based strategy
combinations downward, network focused strategy combinations across
with: green shading, infection attack rate 10 or less; pink shading,
infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827499
.anchor}![](media/image21.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑12. Implementation Threshold 100
Diagnosed Infection Attack Rates, Regionally Unmitigated, 90%
compliance. For Ferguson-like disease manifestation. Case based strategy
combinations downward, network focused strategy combinations across
with: green shading, infection attack rate 10 or less; pink shading,
infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827500
.anchor}![](media/image22.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑13. Implementation Threshold 100
Diagnosed Infection Attack Rates, Regionally Unmitigated, 60%
compliance. For Ferguson-like disease manifestation. Case based strategy
combinations downward, network focused strategy combinations across
with: green shading, infection attack rate 10 or less; pink shading,
infection attack rate between 10% and 25%.

### Administering Pre-Pandemic Vaccine:

Vaccination focused on children and teens was found in Glass et al.
(Glass et al., 2005b) to be the most effective strategy in this social
contact network. Targeting these groups with the full proposed stockpile
(7% of the population or 700 doses in our community of 10,000) of
partially effective vaccine (50% efficacy) yields much greater benefit
than administering it either uniformly throughout age classes or focused
entirely on adults (see full set of tables for this extension are within
[**Appendix E**](#OLE_LINK1)).

In **Tables 4-13, 4-14, 4-15,** and **4-16** the expanding zones of
green and pink show that vaccination targeting children and teens
enlarges the pool of effective (less than 10% and less than 25%
infection attack rate) strategies available for influenza strains at
each IDfactor.

![](media/image23.jpeg){width="3.18125in" height="4.75in"} An example of
this impact can be seen by comparing the vaccine / no vaccine infection
rates in **Figure 4-2.** All four simulations are set to 90% compliance
with an implementation threshold of 10. Those on the left reflect
results in communities with regional mitigation conditions, those on the
right are regionally unmitigated.

The greatest relative benefit is found in the 10 to 25% infection attack
rate zone for no vaccination (pink zone, **top of** **Figure 4-1**)
where vaccination has reduced attack rates by as much as 14%, moving
many of the combined strategies into the green zone (10% or less attack
rate). There, required antiviral courses decreased (up to 47% coverage)
as did days adults are at home (up to 7 days). Within the zone where the
infection attack rate was 10% or less for no vaccination (green zone
**top of Figure 4-1)**, added benefit from targeted vaccination with
pre-pandemic vaccine is in general much less with only small decreases
in antiviral courses given or days adults are at home. However, as we
will see in **Section 5**, the increased benefit afforded by
pre-pandemic vaccination may not end up influencing our design of best
community containment strategy combination.

> []{#__RefHeading___Toc158827158 .anchor}Figure 4‑4. Comparison of
> Infection Attack Rate Tables for combined containment strategies
> without (top) and with (bottom) targeted vaccination of Children and
> Teens.

[]{#__RefHeading___Toc158827501 .anchor}Table 4‑14. Children and
Teenager Targeted Pre-Pandemic Vaccination Infection Attack Rates,
Regionally Mitigated, 90% compliance. For Ferguson-like disease
manifestation, implementation threshold 10 diagnosed, and 700 doses of
50% efficacy pre-pandemic vaccine given to children and teens. Case
based strategy combinations downward, network focused strategy
combinations across ![](media/image24.wmf){width="5.361023622047244in"
height="8.007086614173229in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}with: green shading, infection attack rate
10 or less; pink shading, infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827502
.anchor}![](media/image25.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}Table 4‑15. Children and Teenager Targeted
Pre-Pandemic Vaccination Infection Attack Rates, Regionally Mitigated,
60% compliance. For Ferguson-like disease manifestation, implementation
threshold 10 diagnosed, and 700 doses of 50% efficacy pre-pandemic
vaccine given to children and teens. Case based strategy combinations
downward, network focused strategy combinations across with: green
shading, infection attack rate 10 or less; pink shading, infection
attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827503
.anchor}![](media/image26.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑16. Children and Teenager Targeted
Pre-Pandemic Vaccination Infection Attack Rates, Regionally Unmitigated,
90% compliance. For Ferguson-like disease manifestation, implementation
threshold 10 diagnosed, and 700 doses of 50% efficacy pre-pandemic
vaccine given to children and teens. Case based strategy combinations
downward, network focused strategy combinations across with: green
shading, infection attack rate 10 or less; pink shading, infection
attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827504
.anchor}![](media/image27.wmf){width="5.305511811023622in"
height="8.034645669291338in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑17. Children and Teenager Targeted
Pre-Pandemic Vaccination Infection Attack Rates, Regionally Unmitigated,
60% compliance. For Ferguson-like disease manifestation, implementation
threshold 10 diagnosed, and 700 doses of 50% efficacy pre-pandemic
vaccine given to children and teens. Case based strategy combinations
downward, network focused strategy combinations across with: green
shading, infection attack rate 10 or less; pink shading, infection
attack rate between 10% and 25%.

### Age Class Balanced Transmission: 

Removal of enhanced transmission for the young was found in Glass et al.
(2006) to reduce the efficacy of targeted social distancing of children
and teenagers and, in order to contain infection, to require the
implementation of social distancing within adult groups as well. The
earlier analysis evaluated containment strategy robustness in light of
the removal of enhanced relative infectivity and susceptibility (both
set to 1.0), the increase of contacts within the work environment (by a
factor of 4.0) to put adults on par with children and teens at school,
and the combination of both. Here only the age class balanced uniform
transmission combination given by applying both is analyzed. While we
believe these two characteristics are unlikely to occur even separately,
their combination forms a bounding scenario for extreme infection
transmission rates. For this situation, we ran the full containment
strategy combination matrix with the Ferguson-like disease
manifestation.

**Tables 4-17, 4-18, 4-19, and 4-20**, show the infection attack rates
with less than 10% and 10% to 25% zones colored green and pink,
respectively, as before. As expected, those strategy combinations that
rely on the social distancing of children and teenagers decrease in
efficacy while those that rely on adults increase. While roughly the
same number of strategy combinations are found in both pink and green
zones in each IDfactor region of the 90 and 60% compliance levels for
the regionally uniform policy (**Tables 4-17** and **4-18**),
degradation of efficacy is significant when the community is in contact
with an unmitigated base regional epidemic within surrounding
communities (**Tables 4-19** and **4-20**). This degradation is due to
the increase (by the factor of 4) in the number of contacts within the
work environment, all of which are assumed to take place with adults
from surrounding communities where the epidemic remains unchecked.

Also of interest is the increased sensitivity of the unmitigated base
case attack rate to IDfactor. At IDfactor 0.75, the base epidemic only
attacks 7% of the population (rather than 28% as seen for the base
transmission network emphasizing children and teenagers) and at IDfactor
1.5, 78% are infected (rather than 71% as seen for the base transmission
network).

[]{#__RefHeading___Toc158827505 .anchor}Table 4‑18. Uniform Transmission
Infection Attack Rates, Regionally Mitigated, 90% compliance. For
Ferguson-like disease manifestation and implementation threshold 10
diagnosed. Case based strategy combinations downward, network focused
strategy ![](media/image28.wmf){width="5.364566929133859in"
height="8.0in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}combinations across with: green shading,
infection attack rate 10 or less; pink shading, infection attack rate
between 10% and 25%.

[]{#__RefHeading___Toc158827506
.anchor}![](media/image29.wmf){width="5.301968503937008in"
height="8.041732283464567in"}![](media/image11.jpeg){width="5.95in"
height="0.7137795275590552in"}Table 4‑19. Uniform Transmission Infection
Attack Rates, Regionally Mitigated, 60% compliance. For Ferguson-like
disease manifestation and implementation threshold 10 diagnosed. Case
based strategy combinations downward, network focused strategy
combinations across with: green shading, infection attack rate 10 or
less; pink shading, infection attack rate between 10% and 25%.

[]{#__RefHeading___Toc158827507 .anchor}Table 4‑20. Uniform Transmission
Infection Attack Rates, Regionally Unmitigated, 90% compliance. For
Ferguson-like disease manifestation and implementation threshold 10
diagnosed. Case based strategy combinations downward, network focused
strategy combinations across with: green shading, infection attack rate
10 or less; pink shading, infection attack rate between 10% and 25%.

![](media/image30.wmf){width="5.301968503937008in"
height="8.041732283464567in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}

[]{#__RefHeading___Toc158827508
.anchor}![](media/image31.wmf){width="5.301968503937008in"
height="8.041732283464567in"}![](media/image11.jpeg){width="5.948031496062992in"
height="0.7188976377952756in"}Table 4‑21. Uniform Transmission Infection
Attack Rates, Regionally Unmitigated, 60% compliance. For Ferguson-like
disease manifestation and implementation threshold 10 diagnosed. Case
based strategy combinations downward, network focused strategy
combinations across with: green shading, infection attack rate 10 or
less; pink shading, infection attack rate between 10% and 25%.

# Design Of Effective, Robust Community Containment

The results from simulation studies such as reported above can be used
to design effective, robust containment strategy combinations in the
context of constraints and uncertainties. Below we demonstrate such
design for the level of infectivity consistent with a 1918-like
influenza pandemic, having an IDfactor of 1.5 where \~71% of the
population is infected (\~36% symptomatic) for the base unmitigated
epidemic. Considering first the Ferguson-like disease manifestation with
rapid implementation (10 diagnosed) and 90% compliance, we build our
base design. We then consider the robustness of this design to
implementation threshold, compliance, contact with an external base
epidemic, disease manifestation and social contact network.

## Base design

**Table 5-1** **top** shows the infection attack rate with those
combinations of strategies that yield an infection attack rate below 10%
shaded green and those between 10% and 25% pink.

> Note: an infection attack rate of 10% corresponds to a diagnosed rate
> of 4% and a symptomatic illness rate of 5%. An infection attack rate
> of 25% corresponds to a diagnosis rate of 10% and a symptomatic
> illness rate of 12.5%.

![](media/image8.wmf){width="1.554861111111111in" height="2.0in"}We see
that nearly half of the strategy combinations fall within the
combination of green and pink zones. Implementing all case based
strategies without network focused strategies can yield, at best, an
attack rate of 35%. Implementing all network focused strategies alone
can reduce the attack rate to 5%. Of note is the nonlinearity in the
combination of social distancing strategies. S or CTsd alone are not
very effective, however in combination they reduce the attack rate to
17%, an efficacy much greater than the sum of their singly imposed
reductions. Contrarily, combining S and ASsd reduces the attack rate to
50%, less than the linear combination of their singly imposed
reductions.

Without the use of antivirals, we find 4 effective strategy
combinations: 3 with infection attack rates below 10% and one additional
below 25%. With antivirals many additional combinations can be
implemented; some of which, however, require more treatment courses than
may be available. **Table 5-1 middle** shows the percent coverage of the
population with antivirals (number of courses given as a percent of the
population). Attack rate based coloring has been maintained and those
strategies that require less than 4% coverage (US stockpile estimate at
the end of the summer 2006) are noted with a yellow circle while those
that require up to 25% coverage (planned stockpile estimate for third
quarter 2007) are noted with a red circle. Significant amounts of
antivirals are required to implement any of the PEx strategies; to be
effective, antiviral treatment must be implemented in combination with
S+CTsd and S+CTsd+ASsd. However, we see that PEx is not required at this
IDfactor because treatment alone with either of these two effective
social distancing strategy combinations is sufficient to yield an attack
rate below 10% and with 2% or less coverage of the population.

**Table 5.1 bottom** illustrates the number of days adults remain at
home, whether sick, tending sick children, minding children sent home
from school, or quarantined. We superimpose the intersection of colored
squares (attack rates 25% or less) and colored circles (antiviral
coverage 25% or less) with the average number of adult-at-home days. For
the unmitigated epidemic, adults are home 3 days and approximately 70
people die. For containment strategies utilizing \< 4% antiviral
coverage and yielding infection attack rates of 10% or less (green
zone), adults stay at home ranging from about 6 days (with 2 deaths for
S+CTsd+ASsd combined with P) to 19 days (with 9 deaths for S+CTsd
combined with Q). Adding Q to the combined strategies is of little aid
and has high social costs. Thus, full social distancing (S+CTsd+ASsd)
combined with P is the best choice for design under current constraints
with or without a limited stockpile of antiviral courses.

[]{#__RefHeading___Toc158827509 .anchor}Table 5‑22. Base Community
Containment Design. Ferguson-like disease manifestation, 90% compliance,
IDfactor 1.5, implementation threshold 10 diagnosed, mitigation strategy
combination implemented regionally. Case based strategy combinations
downward, network focused strategy combinations across with: green
shading, infection attack rate 10 or less; pink shading, infection
attack rate between 10% and 25%; yellow circle, antiviral courses less
than ![](media/image32.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image33.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image34.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}4% coverage; red circle, antiviral courses
between 4% and 25% coverage.

## Pre-Pandemic Vaccination:

If we now consider the use of pre-pandemic vaccine at proposed U.S.
stockpile levels (7%, 700 doses in our community of 10000) with assumed
efficacy of 50%, we find little or no added benefit for uniform (**Table
5.2**) or adult targeted (**Table 5.3**) vaccination. However, if we
target the children and teens with all vaccine available to this
community (**Table 5.4**), we find some benefit; the strategy
combinations of S + CTsd and S+ASsd+Q+T implemented with a limited
antiviral stockpile (yellow circles) move into the 10% or lower
infection attack rate (green) zone.

However, *the best strategy choice remains S+CTsd+ASsd+P* with the
infection attack rate, deaths and the number of days adults are home
uninfluenced. Further studies should consider if a stockpile size above
the current proposed 7% coverage with 50% effective pre-pandemic vaccine
would have added benefit and change the choice of best community
containment strategy.

[]{#__RefHeading___Toc158827510 .anchor}Table 5‑23. Pre-Pandemic
Vaccination of General Population. Ferguson-like disease manifestation,
90% compliance, IDfactor 1.5, implementation threshold 10 diagnosed,
mitigation strategy combination implemented regionally, uniform
vaccination of population with 700 doses of 50% efficacy pre-pandemic
vaccine. Case based strategy combinations downward, network focused
strategy combinations across with: green shading, infection attack rate
10 or less; pink shading, infection attack rate between 10% and
![](media/image35.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image36.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image37.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}25%; yellow circle, antiviral courses less
than 4% coverage; red circle, antiviral courses between 4% and 25%
coverage.

[]{#__RefHeading___Toc158827511
.anchor}![](media/image38.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image39.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image40.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}Table 5‑24. Targeted Pre-Pandemic
Vaccination of Adults. Ferguson-like disease manifestation, 90%
compliance, IDfactor 1.5, implementation threshold 10 diagnosed,
mitigation strategy combination implemented regionally, targeted
vaccination of adults with 700 doses of 50% efficacy pre-pandemic
vaccine. Case based strategy combinations downward, network focused
strategy combinations across with: green shading, infection attack rate
10 or less; pink shading, infection attack rate between 10% and 25%;
yellow circle, antiviral courses less than 4% coverage; red circle,
antiviral courses between 4% and 25% coverage.

[]{#__RefHeading___Toc158827512
.anchor}![](media/image41.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image42.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image43.wmf){width="4.74015748031496in"
height="1.7692913385826772in"}Table 5‑25. Targeted Pre-Pandemic
Vaccination of Children and Teenagers. Ferguson-like disease
manifestation, 90% compliance, IDfactor 1.5, implementation threshold 10
diagnosed, mitigation strategy combination implemented regionally,
targeted vaccination of children and teen with 700 doses of 50% efficacy
pre-pandemic vaccine. Case based strategy combinations downward, network
focused strategy combinations across with: green shading, infection
attack rate 10 or less; pink shading, infection attack rate between 10%
and 25%; yellow circle, antiviral courses less than 4% coverage; red
circle, antiviral courses between 4% and 25% coverage.

## Robustness 

The importance of implementing the base design strategy combination
quickly is shown in **Tables 5-5 and 5-6**.

Delaying implementation until 30 people are diagnosed still yields
strategy combinations that provide infection attack rates of 10% or less
(shaded green) and can be accomplished with a limited antiviral
stockpile (yellow circles), and the number adult days at home only
increase slightly.

Delaying implementation until 100 people are diagnosed erodes efficacy
much more dramatically. A limited antiviral stockpile is no longer
sufficient to implement our best strategy choice (S+CTsd+ASsd+P) and 11%
coverage is required. More importantly, the infection attack rate has
slipped to 13%, deaths have risen from 2 to 11, and adult days at home
have increased from 6 to 12.

Reducing compliance to 60% also significantly erodes efficacy (**Table
5-7**). Our best choice remains S+CTsd+ASsd+P, but the infection attack
rate has increase fivefold to 10% with a concurrent increase in the
number of deaths from 2 to 9. Almost 7% antiviral coverage is required
and the number of adult days at home increases to 21, 7 times the
average period for the unmitigated epidemic.

When in contact with surrounding communities in which the unmitigated
base epidemic is running its course, we find our best choice combination
(S+CTsd+ASsd+P) remains the same (**Table 5-8**). If a local community
implements this strategy at 90% compliance after 10 people are
diagnosed, the infection attack (and death) rate will quadruple relative
to the regionally mitigated scenario, but the implementing community can
hold the rate down to 10% or less (green). Antiviral requirements will
increase to 9% coverage and the days adult are at home nearly double.

If we implement the Longini-like disease manifestation (**Table 5-9**),
our choice of strategy combination again remains the same as that found
for the Fergusion-like manifestation; however the cost in terms of adult
days at home nearly doubles (to 10 days) for S+CTsd+ASsd+P.

Finally, if we assume the bounding case of uniform transmission, our
best choice remains unaltered (**Table 5-10**) with fewer than 2%
infected, 2% antiviral coverage required, and only 7 adult days at home.
Thus our best choice, S+CTsd+ASsd+P, is robust to a transmission
perturbation far from what is considered likely.

[]{#__RefHeading___Toc158827513 .anchor}Table 5‑26. Robustness:
Relaxation of Implementation Threshold to 30 Diagnosed. Ferguson-like
disease manifestation, 90% compliance, IDfactor 1.5, implementation
threshold 30 diagnosed, mitigation strategy combination implemented
regionally. Case based strategy combinations downward, network focused
strategy combinations across with: green shading, infection attack rate
10 or less; pink shading, infected
![](media/image44.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image45.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image46.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}attack rate between 10% and 25%; yellow
circle, antiviral courses less than 4% coverage; red circle, antiviral
courses between 4% and 25% coverage.

[]{#__RefHeading___Toc158827514
.anchor}![](media/image47.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image48.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image49.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}Table 5‑27. Robustness: Relaxation of
Implementation Threshold to 100 Diagnosed. Ferguson-like disease
manifestation, 90% compliance, IDfactor 1.5, implementation threshold
100 diagnosed (1% of population), mitigation strategy combination
implemented regionally. Case based strategy combinations downward,
network focused strategy combinations across with: green shading,
infection attack rate 10 or less; pink shading, infection attack rate
between 10% and 25%; yellow circle, antiviral courses less than 4%
coverage; red circle, antiviral courses between 4% and 25% coverage.

[]{#__RefHeading___Toc158827515
.anchor}![](media/image50.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image51.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image52.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}Table 5‑28. Robustness: Relaxation of
compliance to 60%. Ferguson-like disease manifestation, 60% compliance,
IDfactor 1.5, implementation threshold 10 diagnosed (0.1% of
population), mitigation strategy combination implemented regionally.
Case based strategy combinations downward, network focused strategy
combinations across with: green shading, infection attack rate 10 or
less; pink shading, infection attack rate between 10% and 25%; yellow
circle, antiviral courses less than 4% coverage; red circle, antiviral
courses between 4% and 25% coverage.

[]{#__RefHeading___Toc158827516
.anchor}![](media/image53.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image54.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image55.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}Table 5‑29. Robustness: Regionally
Unmitigated Epidemic. Ferguson-like disease manifestation, 90%
compliance, IDfactor 1.5, implementation threshold 10 diagnosed,
community connected to external region with unmitigated base epidemic.
Case based strategy combinations downward, network focused strategy
combinations across with: green shading, infection attack rate 10 or
less; pink shading, infection attack rate between 10% and 25%; yellow
circle, antiviral courses less than 4% coverage; red circle, antiviral
courses between 4% and 25% coverage.

[]{#__RefHeading___Toc158827517
.anchor}![](media/image56.wmf){width="4.756299212598425in"
height="2.661811023622047in"}![](media/image57.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}![](media/image58.wmf){width="4.756299212598425in"
height="1.7755905511811023in"}Table 5‑30. Robustness: Longini-like
Disease Manifestation. Longini-like disease manifestation, 90%
compliance, IDfactor 1.5, implementation threshold 10 diagnosed,
mitigation strategy combination implemented regionally. Case based
strategy combinations downward, network focused strategy combinations
across with: green shading, infection attack rate 10 or less; pink
shading, infection attack rate between 10% and 25%; yellow circle,
antiviral courses less than 4% coverage; red circle, antiviral courses
between 4% and 25% coverage.

[]{#__RefHeading___Toc158827518
.anchor}![](media/image59.wmf){width="4.74015748031496in"
height="2.651968503937008in"}![](media/image60.wmf){width="4.74015748031496in"
height="1.7692913385826772in"}![](media/image61.wmf){width="4.74015748031496in"
height="1.7692913385826772in"}Table 5‑31. Robustness: Uniform
Transmission. Ferguson-like disease manifestation, 90% compliance,
IDfactor 1.5, implementation threshold 10 diagnosed, mitigation strategy
combination implemented regionally, uniform transmission. Case based
strategy combinations downward, network focused strategy combinations
across with: green shading, infection attack rate 10 or less; pink
shading, infection attack rate between 10% and 25%; yellow circle,
antiviral courses less than 4% coverage; red circle, antiviral courses
between 4% and 25% coverage.

# Recommendations For Policy 

In this study we have applied a community scale model that simulates the
spread of influenza in an explicit, multiply overlapping network of
social contacts within a stylized community. The modeled community can
be isolated or embedded within a regional epidemic where other
communities are either imposing the same containment strategies or doing
nothing to abate the epidemic.

By focusing on a single community, we have been able to evaluate an
extensive matrix of containment strategy combinations and disease
infectivity levels. This exploration has enabled us to identify
community containment strategies that minimize illness, death, and loss
of workforce in the face of constrained antiviral or pre-pandemic
vaccine supplies.

Building on this foundation, we have assessed the robustness of
containment designs to variations in disease manifestation, social
network configuration, strategy implementation threshold, public
compliance, and neighboring community behavior.

Based on the findings of this study, we summarize recommendations for
policy in three areas: 1) requirements of robust effective community
containment, 2) necessity of uniform national policy, and 3)
administration of pre-pandemic vaccine. Summary recommendations are also
made for the continued evaluation and reduction of uncertainty.

## Requirements of robust effective community containment strategies

For a 1918-like pandemic infectivity level, strategies can be found that
are effective at both minimizing illness to below 5% of the population
(with nearly no deaths), require levels of antiviral coverage currently
within US stockpiles, and limit cost in terms of adult days spent at
home to below a week (about double the amount of time for the
unmitigated epidemic).

These strategies are robust to both changes in the social contact
network that remove enhanced transmission by children and teenagers and
changes in the disease manifestation within the range currently used in
modeling studies found in the literature. However, strategy
effectiveness depends on rapid implementation and a high degree of
public compliance both for social distancing measures and antiviral
treatment and home prophylaxis. The latter encompasses both
administration of antiviral drugs by the health care infrastructure and
use by the affected persons within the population.

We find the most important component of effective strategy combinations
is the implementation of social distancing with high compliance. For an
infectivity similar to that of the 1918 pandemic, administering
antiviral prophylaxis at levels above 3% coverage adds no benefit and
does not remove the necessity of implementing high compliance social
distancing which includes closing schools. Closing schools imposes the
largest cost in days adults are at home. However, containment strategies
that combine closing schools *and* implementing social distancing of
children and teens are very effective when layered with home antiviral
prophylaxis. By adding implementation of social distancing by adults and
seniors (including a 50% reduction in contacts at work), adult days at
home can be further reduced by a third to an average of 6 per adult.

Thus, social distancing forms the foundation for effective community
containment. Alone it may be able to hold a pandemic at bay; in
combination with case based strategies such as home prophylaxis, death
and days adults are at home can be minimized.

But we restate: strategies must be implemented quickly and with high
compliance. The *critical recommendation for policy* is that planning,
education, and training must be designed for the effective triggering
and implementation of high compliance social distancing measures *first*
and case-based strategies *second*. This conclusion contradicts the
emphasis within the medical and public health community over the past
years where antiviral prophylaxis has been the primary consideration. An
important component for high compliance social distancing among children
will be societal support of families with young as they will bear the
vast majority of the costs of adults days at home. Such a redistribution
of burden could be accomplished through mechanisms including private
(company business plans, insurance policies), public (community
organization, taxation), and not-for-profit resources.

## Necessity of a Uniform National Policy

Isolated communities implementing effective community containment
strategies and communities embedded within regions implementing
effective community containment strategies perform identically. However,
our simulations in which communities implementing containment strategies
are embedded in a region that is doing nothing to abate the epidemic
("regionally unmitigated" with full contact through the work place) show
the importance of regional implementation of community containment
strategies. Without such regional policy, the best community containment
strategy (full social distancing layered with household anitiviral
prophylaxis and 90% compliance) still reduces infectious attack rates
below 10%. However the attack and death rates quadruple from their
values for the regionally mitigated epidemic as have antiviral
requirements (to 9% coverage, well above the current stockpile of
oseltamivir of 7.2% in January, 2007 ("Antivirals-State Allocations,"
2007)), and the number of days adults are at home are doubled. While the
stockpile is set to grow to 25% by the end of 2008, recent data from
H5N1 cases in Egypt have shown that resistance to oseltamivir is already
developing ("Avian Influenza-situation in Egypt," 2007). Thus, leaving
mitigation policy up to individual communities could cost the nation a
great deal. The *critical recommendation for policy* is that a *uniform
national policy* should be imposed and supported for the benefit of all.

## Administration of Pre-pandemic Vaccine 

Administration of pre-pandemic vaccination at proposed stockpile levels
(7% coverage and 50% efficacy) influences the spread of disease somewhat
when children and teens are targeted, as shown in our simulations to be
the most optimal focus. However, if the best community containment
strategy is implemented (full social distancing layered with household
antiviral prophylaxis and 90% compliance), pre-pandemic vaccine affords
no added benefit. Thus, the *critical recommendation for policy* is that
pre-pandemic vaccine, if available at such low levels and efficacy,
should be used primarily to *assure that critical infrastructures
continue to function* during the period of the pandemic. For highest
community benefit, people in positions that cannot be replaced in
infrastructures which must remain operable (such as healthcare and first
responders) should be given the pre-pandemic vaccine. The vaccine will
both decrease the probability of them falling ill and increase the
probability of them continuing to work. Future studies should consider
if a stockpile size above the current proposed 7% coverage with 50%
effective pre-pandemic vaccine would yield enough benefit to change the
choice of best community containment strategy.

## Continued evaluation and reduction of uncertainty 

As has been pointed out by the recent NAS/IOM review of Modeling
Community Containment for Pandemic Influenza (IOM/NAS, 2006), much work
remains to evaluate the uncertainty of community containment efficacy.
Simulation studies such as ours can aid in evaluating uncertainty and in
reducing this uncertainty over time. The current study has taken a step
forward along this path and developed a baseline set of results for
evaluation. Future studies should systematically consider parametric
assumptions for the underlying disease manifestations, social contact
network, the action of antiviral drugs, and containment strategy
implementation. The following outline notes our assessment of the most
important components in each of these areas.

Disease manifestation including:

-   Behavior of infectivity in time

-   Transmission mechanism (aerosol, particles, surface contact)

-   Disease stages and their mean times

-   Fraction asymptomatic (invisible vs visible infected)

-   Mortality

Social contact network including:

-   Sub group network: structured to fully mixed

-   Groups: augmented, relative importance, and makeup (households,
    neighborhoods/extended families, schools, work, clubs, church,
    public transport, etc)

-   Location conditions of possible critical importance (College
    campuses, military reservations, high rises, etc)

-   Collection & incorporation of contact network data

-   Instantiation from community data

Antiviral influences and administration including:

-   Reduction of infectivity (variation with time administered,
    treatment, prophylaxis)

-   Reduction of susceptibility for prophylaxis (variation with time
    administered)

-   Reduction of fraction symptomatic for prophylaxis (variation with
    time administered)

Containment strategy implementation including:

-   Reactive behavior on the part of individuals and communities to
    evaluate compliance with strategy components and design of
    incentives (social modeling)

Modification of community scale models and subsequent analytic sweeps of
parameter space are feasible to evaluate the uncertainty imposed by
extension to the components listed above. Additionally, analysis can be
refined in response to evolving constraints and changes in uncertainty
from data collected as new influenza strains emerge and combined
strategy implementations are undertaken. Ongoing work in this area
should include and *emphasize community scale modeling* in addition to
modeling at the regional or national scales. Modeling activities at all
scales should continue into the indefinite future and work to fully
integrate with economic analysis and detection/monitoring systems for
influenza.

[]{#__RefHeading___Toc158828243 .anchor}References

[]{#__RefHeading___Toc158828245 .anchor}Appendix A: Design of Targeted
Social Distancing Strategies For Pandemic Influenza

Glass, R. J., L. M. Glass, et al. (2006). \"[**Design of Targeted Social
Distancing Strategies for Pandemic
Influenza.**](../AppendixA-EID-06-0255.pdf)\" *Emerging Infectious
Diseases*.

[]{#__RefHeading___Toc158828246 .anchor}Appendix B: WHHSC PIP Simulation
Outline

**[WHHSC PIP simulation outline](../AppendixA-EID-06-0255.pdf)** with
annotations and yellow highlighting to show connection to current
analyses reported here

[]{#__RefHeading___Toc158828247 .anchor}Appendix C: Unmitigated Base
Case Analysis

[]{#OLE_LINK2 .anchor}Analysis of the unmitigated base case for both
Ferguson-like and Longini-like disease manifestations is complied in the
excel worksheet:

[**UnmitigatedBaseCase.xls**](../UnmitigatedBaseCase.xls)

[Within this worksheet the infectious contact sequences generated from
100 runs are analyzed to obtain:](../UnmitigatedBaseCase.xls)

1.  Branching factors by age class and generation;

2.  Maximum branching factors by age class and overall;

3.  Overall branching factor for combined population of 1M people by
    generation and its maximum below generation 10 (approximates *R~o~*,
    see (Glass et al., 2006));

4.  Generation time by age class and generation;

5.  Generation time by age class (averaged over generation);

6.  Average generation time over all age classes;

7.  Fraction of total transmission within and between each age class;

8.  Fraction of total transmission within each group type;

Additionally summary statistics are compiled in the worksheet for

9.  Infection attack rates, illness attack rates, death rates by age
    class and overall;

10. Peak infected, peak symptomatic;

11. Number of epidemics;

12. Timescales: times to peak, epidemic duration, total time;

13. Days adults are home.

The Ferguson-like disease manifestation was used in Targeted Social
Distancing Design for Pandemic Influenza (Glass et al., 2006) in
[**Appendix A**](../AppendixA-EID-06-0255.pdf) and results here conform
closely to those with slight differences due to the inclusion of
babysitting within the community. Below we pull from these results to
give observations on the influence of 1) disease manifestation, 2)
IDfactor, and 3) compliance.

*Observations on Disease Manifestation:*

-   No difference in summary measures of total infected (or symptomatic)
    by age class or overall

-   Longini-like slightly higher for peak infected and peak symptomatic

-   Longini-like \~33% longer time scale and so times to peak, epidemic
    duration and total time of effects

-   Longini-like greater than 50% larger adult days out

-   See plots below

![](media/image62.wmf){width="4.879861111111111in"
height="3.2506944444444446in"}

![](media/image63.wmf){width="4.870138888888889in"
height="3.252083333333333in"}

![](media/image64.wmf){width="4.879861111111111in"
height="3.247916666666667in"}

*Observations on IDfactor:*

-   Increasing IDfactor increases the attack rates, peak values for
    infected and symptomatic and the number of days adults are at home
    while decreasing the times to peak and total time of the epidemic.

-   Increasing IDfactor also shifts the from-to contact fractions
    towards adults and the infectious context fraction from household
    and school to neighborhood and work. These shifts occur because the
    branching factors for adults are pushed above 1 as IDfactor
    increases and so adults become a primary substrate for transmission
    in addition to children and teens.

-   See plots below

![](media/image65.wmf){width="4.879861111111111in"
height="3.247916666666667in"}

![](media/image66.wmf){width="4.879861111111111in"
height="3.247916666666667in"}

![](media/image67.wmf){width="4.879861111111111in"
height="3.247916666666667in"}

*Observations on 90% and 60% compliance:*

-   Compliance has essentially no influence on results once ID has been
    tuned to a 50% infection attack rate except that a change from 90%
    to 60% compliance shifts infectious contact fraction a bit (\~3-5%)
    from household to non-household contexts. This is consistent with
    the increase in non-household contacts at 60%

-   compliance. (see plot below)

![](media/image68.wmf){width="5.258333333333334in" height="3.5in"}

[]{#__RefHeading___Toc158828248 .anchor}Appendix D: Base Containment
Strategy Combination Matrix Results

[]{#OLE_LINK3 .anchor}Statistical measures over 100 runs for the base
matrix of containment strategy combinations are complied in two Excel
workbooks separated as averages and standard deviations (SD):

[FergusonEpidemicCases.xls](../FergusonEpidemicCases.xls)

[FergusonEpidemicCases-SD.xls](../FergusonEpidemicCases-SD.xls)

[The first worksheet of each Excel workbook contains a stand alone
description of the simulation matrix and what is contained within the
worksheet. Subsequent worksheets create a set 3D bar graphs and tables
for the following 15 measures:](../FergusonEpidemicCases-SD.xls)

1.  number of simulations that yield epidemics (defined as \> 1% of
    population infected);

2.  infection attack rate;

3.  illness attack rate;

4.  deaths;

5.  peak infected;

6.  time to peak infected;

7.  peak symptomatic;

8.  time to peak symptomatic;

9.  epidemic duration (from first 10 diagnosed to last diagnosed);

10. total time of effects (from initial seeding to last person
    recovered);

11. number of days strategies imposed;

12. number of mitigation cycles;

13. number of external infections;

14. number of antiviral courses given;

15. number of days adults are at home (either sick, quarantined, or
    tending sick or sent home from school children).

In each 3D bar graph and table, strategies are organized with network
focused strategy combinations of S, CTsd, and ASsd in columns and case
based strategy combinations Q, T, P, and Pex in rows yielding the 64
possible strategy combinations at each of 7 IDfactors. To aid in viewing
this data, those combinations that yield an attack rate that is 10% or
less are shaded green and those up to 25% are shaded pink in the tables.

Time series plots for daily measures averaged over the set of 100
simulations may be made for any of the combinations of strategy (64),
IDfactor (7), compliance (2) boundary condition (2) or disease
manifestation (2). An example set of such time series plots for IDfactor
of 1.5 and Ferguson-like disease manifestation that consider the
measures of people infected, given antiviral, adults at home, and
symptomatic are presented in the following files:

[Sequence1.5-90.pdf](../Sequence1.5-90.pdf)

[Sequence1.5-60.pdf](../Sequence1.5-60.pdf)

[Sequence1.5-90ExternalBaseEpidemic.pdf](../Sequence1.5-90ExternalBaseEpidemic.pdf)

[Sequence1.5-60ExternalBaseEpidemic.pdf](../Sequence1.5-60ExternalBaseEpidemic.pdf)

[]{#OLE_LINK1 .anchor}Appendix E: Matrix Extension Results

Four extensions to the base containment strategy combination matrix were
considered:

1)  natural history disease manifestation: Longini-like (Germann et al.,
    2006; Longini et al., 2005).

2)  2 relaxed implementation thresholds (day after 30 or 100 diagnosed
    within the community);

3)  3 pre-pandemic vaccination strategies with 7% coverage of 50%
    efficacy vaccine administered: randomly, targeted to children and
    teens, or targeted to adults.

4)  Uniform transmission within children, teens, and adults (uniform
    relative infectivity and susceptibility and identical number of
    contacts within workplaces and schools).

For each extension, 100 runs for the full set of 64 containment strategy
combinations, 7 IDfactors, 2 compliances (90%, 60%) and two boundary
conditions (with or without connection to external unmitigated epidemic)
were conducted. Statistical measures over 100 runs are complied in Excel
workbooks separated as averages and standard deviations:

**Excel files for Longini-like disease manifestation:**

[LonginiEpidemicCases.xls](../LonginiEpidemicCases.xls)

[LonginiEpidemicCases-SD.xls](../LonginiEpidemicCases-SD.xls)

**Excel files for implementation threshold relaxation:**

[FergusonT1EpidemicCases.xls](../FergusonT1EpidemicCases.xls)

[FergusonT1EpidemicCases-SD.xls](../FergusonEpidemicCases-SD.xls)

[FergusonT2EpidemicCases.xls](../FergusonT2EpidemicCases.xls)

[FergusonT2EpidemicCases-SD.xls](../FergusonT2EpidemicCases-SD.xls)

**Excel files for pre-pandemic vaccination:**

[FergusonV1EpidemicCases.xls](../FergusonV1EpidemicCases.xls)

[FergusonV1EpidemicCases-SD.xls](../FergusonV1EpidemicCases-SD.xls)

[FergusonV2EpidemicCases.xls](../FergusonV2EpidemicCases.xls)

[FergusonV2EpidemicCases-SD.xls](../FergusonV1EpidemicCases-SD.xls)

[FergusonV3EpidemicCases.xls](../FergusonV3EpidemicCases.xls)

[FergusonV3EpidemicCases-SD.xls](../FergusonV3EpidemicCases-SD.xls)

**Excel files for uniform transmission:**

[FergusonU1EpidemicCases.xls](../FergusonU1EpidemicCases.xls)

[FergusonU1EpidemicCases-SD.xls](../FergusonU1EpidemicCases-SD.xls)

As in **Appendix D**, the first worksheet of each Excel workbook
contains a stand alone description of the simulation matrix and what is
contained within the worksheet. Subsequent worksheets create a set 3D
bar graphs and tables for the following 15 measures:

1.  number of simulations that yield epidemics (defined as \> 1% of
    population infected);

2.  infection attack rate;

3.  illness attack rate;

4.  deaths;

5.  peak infected;

6.  time to peak infected;

7.  peak symptomatic;

8.  time to peak symptomatic;

9.  epidemic duration (from first 10 diagnosed to last diagnosed);

10. total time of effects (from initial seeding to last person
    recovered);

11. number of days strategies imposed;

12. number of mitigation cycles;

13. number of external infections;

14. number of antiviral courses given;

15. number of days adults are at home (either sick, quarantined, or
    tending sick or sent home from school children).

In each 3D bar graph and table, strategies are organized with network
focused strategy combinations of S, CTsd, and ASsd in columns and case
based strategy combinations Q, T, P, and Pex in rows yielding the 64
possible strategy combinations at each of 7 *IDfactors*. To aid in
viewing this data, those combinations that yield an attack rate that is
10% or less are shaded green and those up to 25% are shaded pink in the
tables.

Time series plots for daily measures averaged over the set of 100
simulations may be made for any of the combinations of strategy (64),
*IDfactor* (7), compliance (2) boundary condition (2) or disease
manifestation (2) but have not been included in this report.

[]{#__RefHeading___Toc158828250 .anchor}Appendix F: Presentation To The
Institute Of Medicine

Design of Community Containment for Pandemic Influenza, R.J. Glass, H.J.
Min, W.E Beyeler and L.M. Glass

Presented at the review by Institute of Medicine of the National
Academies on

"Modeling Community Containment for Pandemic Influenza"

October 24, 2006

[AppendixF-RJG-Loki-Infect-IOM.pdf](../AppendixF-RJG-Loki-Infect-IOM.pdf)

[]{#__RefHeading___Toc158828251 .anchor}Appendix G: Additional Points Of
Discussion

[]{#OLE_LINK4 .anchor}

**Why do targeted social distancing strategies (S, CTsd, ASsd) work?**

Targeted social distancing strategies work by pushing the infectious
contact network below the percolation threshold such that any
instigation does not lead to a network spanning event (epidemic).
Schools form the highest zone of infectious contact and contacts there
between children and teenagers first rise above the percolation
threshold as *I~D~* increases. Removal of these contacts for an
*IDfactor* of 1.0 does not quite push the infectious contact network
below the percolation threshold. However the additional reduction of
extra-curricular contacts for children and teenagers does, even at an
*IDfactor* of 1.5 (for a compliance of 90%). Increasing *I~D~* further
allows other portions of the heterogeneous contact network to rise above
the percolation threshold as well and thus support a network spanning
epidemic on their own. At an *IDfactor* of 2.0, adult and senior social
distancing is also required and would need to be above the
50% compliance used in the current simulations to push the network below
the percolation threshold. As an example, distancing all non-household
adult and senior groups by 90% while maintaining full work contacts for
adults is sufficient to reduce the attack rate below 10% for an
*IDfactor* of 2.0.

**Why/When do case based containments (Q, T, P, Pex) work or not work?**

While social distancing strategies can be effective under all conditions
if imposed quickly enough, pervasively enough, and with high enough
compliance, case based containments are not. In case based containment,
the portion of the contact network connected to the identified case is
*illuminated* and contained either through quarantine, isolation, or
prophylaxis with drugs. Such a strategy will be effective if the
illuminated zone captures all infectious contacts resulting from the
identified case. Satisfying this criterion requires that the speed of
disease progression is slow enough that when case based containment is
applied, the required containment zone has not expanded too far. The
speed of disease progression depends on how close the infectious contact
network is to the percolation threshold. As the network approaches the
percolation threshold from above, the speed at which the disease spreads
decreases and reaches a minimum at the threshold. Thus, case based
containments work best at or just above the percolation threshold where
there is both time for implementation and the zone of containment is
local. This requirement for effectiveness is clearly seen in the
simulation data within **Tables 4-1, 4-2, 4-5, 4-6**. Where social
distancing strategies alone have pushed the attack rate to \~40% and
below, adding case based containments drop the rate to below 10%.

A second and at first glance confounding issue with both normal and
historical pandemic influenza strains is that infectious cases are not
all identifiable through symptoms. For influenza, both a pre-symptomatic
infectious state and a non-symptomatic infectious state occur to thwart
detection. In the current model formulated to 1) reasonably fit the
viral shedding data of Hayden, 2) yield a period for a pre-symptomatic
infectious state of 0.5 days before the onset of symptoms, and 3)
constrain only half of those that are infected to become symptomatic, a
full 2:1 ratio of unknown to known infectious contacts occur within the
population at large (where known is defined as those that take place
during the symptomatic infectious period). Such a high ratio would
suggest that case based containment strategies would be very
ineffective. But, because unknown infectious agents are associated with
known infectious agents, case based containment is still effective as
long as the speed of disease spread is slow enough that all
pre-infectious cases fall within the containment zone and can be
neutralized.