Necessary and sufficient conditions for exact closures of epidemic equations on configuration model networks

Istvan Zoltan Kiss, Eben Kenah & Grzegorz A. Rempała
Springer Link
Journal of Mathematical Biology volume 87, Article number: 36
August 2, 2023


We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative binomial distribution. The proof relies on establishing the equivalence, for these specific degree distributions, between the closed pairwise model and a dynamical survival analysis (DSA) model that was previously shown to be exact. Specifically, we demonstrate that the DSA model is equivalent to the well-known edge-based Volz model. Using this result, we also provide reductions of the closed pairwise and Volz models to a single equation that involves only susceptibles. This equation has a useful statistical interpretation in terms of times to infection. We provide some numerical examples to illustrate our results.

Related publications