For the base case, stochasticity is introduced by conducting Bernoulli trials and generating _N_ uniform [0, 1] numbers for _N_ mixing groups. If the probability for an individual to be infected on a day in that group<sup>36</sup> is greater than the random number, then a single infected individual in his/her latent period is ‘introduced’ into each of _N_ mixing groups at model inception. Secondary infections result in each mixing group that has an infected individual. Similar to ‘hierarchical epidemic’ models, this within mixing group dynamic is extended to between‐group analysis. The spread to mixing groups without primary introductions is modeled, based on assumptions and distance from infected groups. Each stochastic realization, for a certain _R0_ , leads t an overall attack rate. o Such stochastic‐spatial models are computationally intensive if populated with millions of individuals, but can evaluate public health interventions such as quarantines and social distancing, ring prophylaxis (where a fixed percentage of people in an _x_ square mile radius around an outbreak are given antivirals), and vaccination. Similar models, but with different assumptions and techniques, have also been constructed for Thailand<sup>5</sup> , the US and UK<sup>37</sup> , and separately for the US<sup>38</sup> . Important differences obtain in whether the model is capped at producing an overall attack rate for a level of _R0_ and i how hn igher _R0_ is reflected.

Stochastic‐spatial models capture population‐level effects by describing the intensity of risk at the individual level. They can also be calibrated to a specific magnitude of GAR from prior pandemics (Longini _et al._ chose to calibrate to 33%, based on the first wave of the 1957 and 1968 pandemics) and a relative attack rate pattern across ages (see Fig. 3 below). As suggested above, the stochastic model produces a distribution of age‐specific and gross attack rates at different _R0_ . By selecting for an overall GAR of 33% and an age‐specific attack rate pattern, Longini _et al._ determine the model seeding that reproduces past pandemics as a base case. They test the intervention strategies thereafter at this setting.

**Fig. 3:** **_Assumed pattern of attack rates across age groups at different R0 (Longini et al. 2005)_**

<!-- Start of picture text --> 0.7<br>0.6 R0<br>R<br>0.5 1.1<br>1.4<br>0.4<br>1.7<br>0.3 2.1<br>2.4<br>0.2<br>0.1<br>0.0<br><1 1-5 6-10 11-14 15-17 18-44 45-64 65+<br>Age<br>*Pattern is based on US data from 1957‐58 (more children infected) and 1968 (similar attack rates across ages)<br>pandemics, mixed with seasonal influenza data from SE Asia (similar to 1957‐58 pandemic in the US).<br>Infection attack rate<br><!-- End of picture text --> The calibrated stochastic‐spatial technique ensures that the locational and demographic heterogeneity of the epidemic area is captured, while the full range of the stochastic results are capped at past experience. This method is good at predicting whether an epidemic that begins randomly somewhere will spread, and evaluating which control options will be successful in limiting its spread. Table 5 provides a comparison of a model like in Longini _et al._ (2005) and the age‐structured SEIR model portion from a proposed 12