Generalised probability mass function for the final epidemic size of an SIR model on a line of triangles network

Abstract

We explore the feasibility of deriving generalised expressions for the probability mass function (PMF) of the final epidemic size of a Susceptible - Infected - Recovered (SIR) model on a finite network of an arbitrary number of nodes. Expressions for the probability that the infection progresses along a given pathway in a line of triangles (LoT) network are presented. Deriving expressions for the probability that the infection ends at any given node allows us to determine the corresponding final size of the epidemic, and hence produce PMFs of the final epidemic size. We illustrate how we can use the results from small networks derived in a previous study to describe how an infection spreads through a LoT network. The key here is to correctly decompose the larger network into an appropriate assemblage of small networks.