Generalization of Pairwise Models to non-Markovian Epidemics on Networks

Istvan Z. Kiss, Gergely Röst, Zsolt Vizi
2015 Physical Review Letters  
In this letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations (DDEs), which shows excellent agreement with results based on explicit stochastic simulations of non-Markovian epidemics on networks. Furthermore, we analytically compute a new R0-like threshold quantity and an implicit analytical relation between this and the final
more » ... is and the final epidemic size. In addition we show that the pairwise model and the analytic calculations can be generalized in terms of integro-differential equations to any distribution of the infectious period, and we illustrate this by presenting a closed form expression for the final epidemic size. By showing the rigorous mathematical link between non-Markovian network epidemics and pairwise DDEs, we provide the framework for a deeper and more rigorous understanding of the impact of non-Markovian dynamics with explicit results for final epidemic size and threshold quantities.
doi:10.1103/physrevlett.115.078701 pmid:26317749 fatcat:lpjn4ly4hngvzd2k6qzzt2ofem