Large population limit for a multilayer SIR model including households and workplaces

TL;DR

This paper analyzes a multilayer SIR epidemic model with household and workplace contacts, proving large population convergence and deriving a simplified deterministic system that accurately captures epidemic dynamics.

Contribution

It introduces a novel multilayer SIR model with explicit infectious period distributions and provides a rigorous large population limit with a reduced dynamical system.

Findings

Large population convergence established for the stochastic process.

Derived a finite-dimensional deterministic system for exponential infectious periods.

Numerical validation shows the reduced model's accuracy and efficiency.

Abstract

We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population convergence of the corresponding stochastic process. For this purpose, we use an individual-based model whose state space explicitly takes into account the duration of infectious periods. This allows to deal with the natural correlation of the epidemic states of individuals whose household and workplace share a common infected. In a general setting where a non-exponential distribution of infectious periods may be considered, convergence to the unique deterministic solution of a measurevalued equation is obtained. In the particular case of exponentially distributed infectious periods, we show that it is possible to further reduce the obtained deterministic limit, leading to a closed, finite dimensional dynamical system capturing the epidemic dynamics. This model reduction subsequently is studied from a numerical point of view. We illustrate that the dynamical system derived from the large population approximation is a pertinent model reduction when compared to simulations of the stochastic process or to an alternative edgebased compartmental model, both in terms of accuracy and computational cost.