Poisson network SIR epidemic model

We examine a popular extension of the classical Susceptible-Infected-Recovered (SIR) model within a network-based framework, where node degrees follow a Poisson distribution. First, we review the properties of this extension, its connection to the classical SIR model, and its relationship with the pairwise closure condition for stochastic epidemics on networks. We then apply it to data analysis. This network-based formulation introduces an additional parameter representing the mean node degree, allowing for the incorporation of heterogeneity in contact patterns. Using the extended SIR model, we analyze epidemic data from the 2018–2020 Ebola outbreak in the Democratic Republic of the Congo, employing a survival approach combined with the Hamiltonian Monte Carlo method. Our findings suggest that network-based models more accurately capture epidemic heterogeneity than traditional compartmental models, without introducing unnecessary additional complexity.