We define eight expected numbers E s,n of secondary infections per index case which depend on the index case's infectious stage s {prodromal, earlyrash, middlerash, laterash} and on the network n {close, casual} in which the secondary cases are produced (Table S1 ). This distinction enables us to consider a more intense exposure of close contacts and to modify the cases' contagiousness in their different disease stages, as suggested by previous smallpox studies [19, 23] . We set the sum of these expected values to 5, the estimate at smallpox's eradication [24] . In a homogeneously mixing population, this would be called the basic reproduction number R 0 . We have decided to parameterize our model with these expected values rather than the maximum eigenvalue of the next generation matrix, not only because expected values are more intuitive, but also because estimates of R 0 are frequently based on secondary cases [14, 23] or on homogeneous mixing assumptions [25, 26] . As the maximum eigenvalue better predicts the initial spread of an epidemic, we use it in Figure 3 in the results. In the simulation model, we implement the following infection process: when an individual enters one of the four contagious states, it triggers future infection events for each of its contacts. This is done in the following way: (1) we chose the effective contact rate b s,n such that 