# Presentation: 018231

## Modeling potential herd immunity from influenza vaccination

**Martin Meltzer, Ph.D.**
**Office of Surveillance, NCID**

## Why & how model?

**Lack of data**
**No statistical analyses all questions**
**Want extrapolations, interpolations**
**Answer “what ifs”**
**Many methods available**
**Deterministic: fixed relationships**
**Stochastic: probabilities define relationships**** **
**Different levels possible**

## Papers considered: One Model

- Elveback et al: Am J Epidemiol. **1976**; 103:153
- Longini et al: Vaccine, **2000**;18:1902-1909
- Halloran et al. Vaccine **2002**; 20: 3254-3262
- Weycker et al: Vaccine **2005**;23:1284-1293
- Background:
- Longini et al. Internat J Epi **1984**;13:496-501
- Longini et al: Am J Epi **1982**;115:736-751.

## The model(Halloran et al Vaccine 2002 20: 3254-3262)

- 2000 people – age/ gender as per census
- Households in 4 neighborhoods;
- 1 HS, 1 MS, 2 ES, small or large playgroups
- No risk groups by pre-existing conditions
- No nursing homes
- Weyker et al. bigger – 10,000 in 5 neighborhoods
- Individual “agent” level model
- Start: Randomly allocate 12 infectives
- Further introductions – not addressed

## Transmission data: Sources

- Household transmission: Halloran et al:
- Tecumseh; 1977/78 and 1980/81
- (Addy et al., Biometrics 1991;47:961-974)
- Other rates:  “ **. *****. chosen to calibrate . . . to certain illness attack rates in each age group*****.”**
**Young children:  27%     **(95 CI: 2, 42)
**Older children :   29%     **(95 CI: 3, 40)
**Adults (all):          10%     **(95 CI: 2, 14)
**OVERALL:            15%    **(95 CI: 2, 22)
**Wyecker et al – average 11% - sensitivity analysis**
**Elveback et al: 1957 and 1968 pandemics**

## Who infects whom:

- Table 7
- Transmission probabilities in simulated populations
- Contact group 	Children 					Adults
- 		Pre-school 		School 			Younger 	Older
- 		Small play group 	Large daycare 	Elementary 	Middle 	High
- Small play groups 	0.0680 	– 	– 	– 	– 	– 	–
- Large daycare centers 	– 	0.0275 	– 	– 	– 	– 	–
- Elementary school 	– 	– 	0.00577 	– 	– 	– 	–
- Middle school 	– 	– 	– 	0.00477 	– 	– 	–
- High school 		– 	– 	– 	– 	0.00177 	– 	–
- Family
- Child 		0.08 	0.08 	0.08 	0.08 	0.08 	0.03 	0.03
- Adult 		0.03 	0.03 	0.03 	0.03 	0.03 	0.04 	0.04
- Neighborhood 	0.00001 	0.00001 	0.000027 	0.000027 	0.000027 	0.00012 	0.00012
- Community 		0.000005 	0.000005 	0.000015 	0.000015 	0.000015 	0.000115 	0.000115

**Who infects whom:**
**Matrix of transmission probabilities**

- Source: Halloran et al. Vaccine, 2002;20:3254-3262

## Who infects whom: Close up of some daily transmission probabilities

| Contact group | Pre-school | School | Adults |
| --- | --- | --- | --- |
|  | Small play grp | Middle | Younger |
| Small play grp | 0.068 | - | - |
| Large daycare | - | - | - |
| Elementary | - | - | - |
| Middle | - | 0.00477 | - |
| High | - | - | - |
| Family: Child | 0.08 | 0.08 | 0.03 |
| Family: Adult | 0.03 | 0.03 | 0.04 |
| Neighborhood | 0.00001 | 0.000027 | 0.00012 |
| Community | 0.000005 | 0.0000015 | 0.000115 |

- Source: Halloran et al. Vaccine, 2002;20:3254-3262

## Results: Cases averted

| Children vaccinated % | Cases (thousands) |  |  |
| --- | --- | --- | --- |
|  | 0-18 yrs | 19-64 yrs | 65+ |
| Base | 19,691 | 12,597 | 1,722 |
| 20% | 8,661 | 7,125 | 980 |
| 80% | 783 | 1,768 | 262 |

- Base vaccinations:  5% children; 22.9% of 19-64yrs; 68.1% of 65+yrs

- Source: Weycker et al., Vaccine 2005; 23:1284-1293

## Results: EffectivenessMean % (S.D.)

| Coverage in children | Indirect effectiveness |  | Overall effect |
| --- | --- | --- | --- |
|  | Children | Adults | Population |
| 30% | 20 (22) | 23 (20) | 23 (20) |
| 70% | 58 (14) | 59 (13) | 62 (12) |

- Note: Adults vaccinated: 22.9% of 19-64yrs; 68.1% of 65+yrs

- Source: Halloran et al., Vaccine 2002; 20:3254-3262

## Critical fraction f*

- 0.6

- 0.5

- 0.3

- 0.4

**Critical fraction ****f***

- 3.00

- 1.50

- 2.00

- 2.50

**Ro**

**Critical fraction (f*) vs. Ro**
**Efficacy (susceptible) = 92%**

- 0.8

- Efficacy
- infectiousness

**80%**

**0%**

- Source:
- Longini et al
- Vaccine,
- 2000; 18:
- 1902-1909

**% children vaccinated to stop epidemic**

## Some evidence of vaccine-generated herd immunity

- Source: Reichert et al. N Eng J Med 2001;344:889-896

**Some evidence of vaccine-generated herd immunity**

**Start: Japanese vaccination**
**of children**

## Seen pattern before? Infectious Disease Mortality in the United States, 1900 to 1996

- Source: Armstrong et al, JAMA, 1999; 281:61-66

## Background to Japanese experience: Changes in Population Pyramid, Japan, 1950 - 2000

- Age

- Male

- Female

- Male

- Female

- Population (thousands)

- Population (thousands)

**Did such changes alter the transmission matrix in Japan?**
**Account for such changes in U.S. (when data sources are “old”)?**

## Logistics, logistics, logistics

| Delay
(days) | Cases (No./1,000) |  |  | Epi Prevent. Potent |  |
| --- | --- | --- | --- | --- | --- |
|  | Mean | 95% C.I. |  | Mean | 95% C.I. |
| 1 | 23 | 2, 162 |  | 79 | 67, 91 |
| 5 | 182 | 91, 251 |  | 0 | 0, 0 |

**Assume: 80% targeted prophylaxis with anti-viral drugs of contacts of identified cases, for up to 8 weeks**

- Source:  Longini et al., Am J Epidemiol, 2004;159:623-633

## Pandemic vaccination progress toward meeting 80% goal 

**Pandemic vaccination progress toward meeting 80% goal **
**for target groups: 5 million doses available per week****

*** Also, roughly equal to immunizing 80% of all children under the age of 18**
**** Assume no waste and all vaccine goes to 80% of target group**

**Vaccinated Population**** ****(cumulative millions)**

- High Risk
- Pop. Only *
- 85 million

- Medical Care
- Workers Only
- 13.5 million

- High Risk Pop. +
- Medical Care
- 92 million

**2 dose/ person**

**1 dose/ person**

## 3 major concerns

- Confidence intervals
- How wide?  How big a “gamble?”
- Available data indicative of pandemic?
- Transmission matrix “realistic?”
- Logistics a BIG problem
- Delay of 1 -3 months in vaccinating target group?
- Could it actually be done – production delays?

## Appendix

## The model: Part II

- Pre-intervention vaccination rates
- 5% child; 22.9% in 19-64yrs;  68.1% in 65+yrs
- Represents 64.5 million doses adults > 18 yrs.
- Vaccine efficacy:
- Protective (susceptible) efficacy = 70%
- Infectiousness efficacy = 80%
- Intervention: Vaccinate children 1-18yrs
- 30% or 50% or 70%

## The model: Part III

- Latent period: 1-3 days, mean 1.9
- Infectious period: 3-6 days, mean 4.1
- Prob. infective is symptomatic: 67%
- Asymptomatic: 50% are infectious
- Prob. of withdraw, given symptoms
- Pre-school: 80%; school kid 75%; adults 50%
- Withdraw on days 0 through 2

## More ResultsWeycker et al Vaccine 2005; 23: 1284-1293

**Attack rates:**
**0-4 yrs:****	****	****17%**
**5-18 yrs: ****	****	****24%**
**19 + yrs****	****	**** 7%**
**       ****Overall average:****	****11%**** **
**Vaccine efficacy**
**70% susceptibility children & younger adults**
**50% susceptibility older adults**
**80% infectiousness all ages**
**Sensitivity analyses**
- Reduced within house transmission child-to-adult by 50% & increased adult-to-adult

## Summary and Conclusions

- One model/ community = all U.S.?
- Transmission matrix:
- Hold for all years and all communities?
- Some other inputs also kept fixed
- Outside introductions – not explored
- Only sub-divide by age (no risk)
- Vaccinate all children 6 months – 18 yrs
- Vaccinate other age groups – 64.5 mil doses
- Cost of vaccinating children not explored
- In U.S., approx. 77 million children aged <1 – 18 yrs
- Models – demonstrations, not absolute proof

## The model: Transmission

- Each person, each day, prob. of contact:
- Pre-school (2 types); School ( 3 types)
- Family (child; adult);
- Neighborhood; Community
- Calculate probability of transmission