**_Concepts in modeling transmission and control of pandemic influenza_** : The discussion above sets the stage to discuss concepts that in modeling determine whether an infectious disease will be rapidly controllable after the initial emergence of an outbreak:

- The _basic reproduction number R0_ is a measure of the base or intrinsic infectivity of any infectious agent such as an influenza virus. It is defined as the number of secondary infections generated by a primary infection in a homogeneous population where everyone is equally susceptible to infection (complexities in defining _R0_ in a heterogeneous population are omitted). _R0_ is a modeling construct that captures several characteristics of infectivity – the transmission risk per contact, duration of the infectivity period, mode of transmission, etc. – and is difficult to predict in advance of an epidemic. Some estimates of _R0_ for past outbreaks are provided in Table 4.

- The _disease generation time Tg_ is the mean interval between infection of one person and infection of the people that the individual infects14 (Ferguson _et al_ . 2005 use _Tg_ =2.6).

- The _proportion of transmission occurring prior to symptoms_ (i.e., asymptomatically), _θ_ .

The importance of these constructs in modeling can be seen against modern practice in outbreak control. These public health practices – in the absence of effective vaccine or treatment in the prevention of spread – are credited with containing the spread of SARS. The first actions are active surveillance and then the effective isolation of individuals displaying pre‐identified symptoms. The second is the tracing and quarantining of the contacts of the individuals who are displaying symptoms. Success here depends on whether the symptomatic individuals are rapidly identified by authorities (e.g., at airports) or they voluntarily report to a public hea th facilit soon afl y ter their symptoms emerge.

Given the importance paid to contact tracing, symptom‐based screening, and surveillance in discussions on pandemic influenza, it is useful to review the SARS experience. On the plus side, SARS symptoms preceded the peak infectivity period by a few days. There was little evidence of asymptomatic transmission. This implies that _θ_ was low. The outbreaks also happened to occur in cities with well‐functioning public health systems where trust in official communications and measures was high and maintained. In the negatives, the symptom‐based entry screening process at Canadian airports was not found cost‐effective<sup>15</sup> . If _θ_ is low but _R0_ is high (see Table 3) in a SARS‐like outbreak, it may be preferable to rely on surveillance to detect the cases early and then to quarantine quickly.

**Table** **<u>3</u>** : **_Estimates_** **_<u>of important modeling constructs for infectious disease outbreaks</u>_**

|**Disease Outbreak**|_R0_|_θ_|r<br>S<br>ce<br>ou|
|---|---|---|---|
|Pandemic influenza, 1918, New Zealand|1.3<<br>3.1<br>_R0 _<|n.a.|Sertsou_et al._2006<sup>16</sup>|
|Pandemicinfluenza,1918, UK(first wave)|1.7<br>_0_<sup>< 2</sup><br><_R_|n.a.|Ferguson_et al._2006<sup>37</sup>|
|Pandemicinfluenza,1968‐69,HongKong|1.89|n.a.|Rvachev &Longin 1<br>i985<sup>31</sup>|
|Smallpox|4<br>_R0 _<<br><<br>10|0<<br>%<br> _θ_< 20|Eichner&Dietz 2003<sup>17</sup>|
|SARS2003HongKong|2 <_R0 _< 4|<11%|Fraser_et al._2004<sup>14</sup>|

The higher is _R0_ (and lower is _Tg_ ) the quicker do public health authorities need to intervene with screening, case‐patient isolation, and enhanced active surveillance of the population. The higher is _θ,_ the lower the cost‐effectiveness of symptomatic screening. Authorities may not be able to remove infectives fast enough before they cause secondary cases. If a pandemic influenza outbreak occurs, it may be possible to quickly estimate _θ_ from available data on infected people and their contacts. Estimating _R0_ is harder, but together with _θ_ , the parameter would set valuable context for the efficacy of proposed policies. Based on what is known of seasonal influenza as well past influenza pandemics, it is believed that: 5