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## Contagion Process 

<img src='content_image/303990.jpg'>

The contagion process continues for T = 5 time steps. For simplicity, we assume a strong exposure effect that reduces contagious spread: the probability each affected node affects a selected neighbor is p$_{0}$ = 0 . 3 in unexposed clusters and p$_{1}$ = 0 . 1 in exposed clusters. 

## Probability of Cluster Exposure 

The true simulation propensity score, the probability that a given cluster is exposed, is generated by a simple logistic function of a single cluster-level covariate, the number of affected neighbors at baseline summed for all nodes in each cluster (see Equation 3). For each scenario, ψ$_{0}$ and ψ$_{A}$ are selected such that this probability is between 0 . 1 and 0 . 9 for all clusters. In the estimation procedure, the regression used for the exposure propensity model includes this covariate, ensuring asymptotically unbiased estimation of the exposure effect. 

