An epidemic model on a network having two group structures with tunable overlap

TL;DR

This paper models epidemic spread on a network with two overlapping group structures—households and workplaces—using a stochastic SIR model, analyzing outbreak probabilities and sizes as population grows large, with flexible overlap and infectious period distributions.

Contribution

It introduces a generalized epidemic model on a network with tunable overlap between household and workplace groups, extending previous results to more complex and realistic social structures.

Findings

Derived asymptotic probabilities of major outbreaks.

Analyzed the impact of group overlap on epidemic dynamics.

Allowed for arbitrary infectious period distributions.

Abstract

A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is constructed such that a parameter $\theta$ controls the degree of overlap between the two group structures: $\theta=0$ corresponding to all household members belonging to the same workplace and $\theta=1$ to all household members belonging to distinct workplaces. On the network a stochastic SIR epidemic is defined, having an arbitrary but specified infectious period distribution, with global (community), household and workplace infectious contacts. The stochastic epidemic model is analysed as the population size $n\to\infty$ with the (asymptotic) probability, and size, of a major outbreak obtained. These results are proved in greater generality than existing results in the literature by allowing for any fixed $0 \leq \theta \leq 1$, a non-constant infectious period distribution, the presence or absence of global infection and potentially (asymptotically) infinite local outbreaks.