Large graph limit for an SIR process in random network with heterogeneous connectivity

TL;DR

This paper rigorously derives the large population limit of an SIR epidemic model on a random network with heterogeneous connectivity, using measure-valued equations to describe disease dynamics.

Contribution

It provides a rigorous proof of the limiting equations for an SIR process on a configuration model network with heterogeneous degrees, extending prior heuristic results.

Findings

Derived measure-valued equations for disease spread

Proved the large population limit rigorously

Confirmed equations previously obtained by Volz

Abstract

We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz [Mathematical Biology 56 (2008) 293--310].