Poisson Network SIR Epidemic Model

Abstract

We extend the classical Susceptible-Infected-Recovered (SIR) model to a network-based framework where the degree distribution of nodes follows a Poisson distribution. This extension incorporates an additional parameter representing the mean node degree, allowing for the inclusion of heterogeneity in contact patterns. Using this enhanced model, we analyze epidemic data from the 2018-20 Ebola outbreak in the Democratic Republic of the Congo, employing a survival approach combined with the Hamiltonian Monte Carlo method. Our results suggest that network-based models can more effectively capture the heterogeneity of epidemic dynamics compared to traditional compartmental models, without introducing unduly overcomplicated compartmental framework.