A framework for the modelling and the analysis of epidemiological spread in commuting populations

TL;DR

This paper develops a comprehensive mathematical framework for modeling and analyzing epidemic spread in large, regularly commuting populations, integrating classical compartmental models with periodic and structured population dynamics.

Contribution

It introduces a general class of models incorporating time-periodic mixing and provides methods to estimate the basic reproduction number in such systems.

Findings

Framework for modeling epidemic spread in commuting populations.

Methods to compute the basic reproduction number in periodic systems.

Integration of classical models with structured population dynamics.

Abstract

In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly speaking the case in populous urban center. We consider a large number of distinct homogeneous groups of individuals of various sizes, called subpopulations, and focus on the modelling of the changing conditions of their mixing along time and of the induced disease transmission. We propose a general class of models in which the 'force of infection' plays a central role, which attempts to 'reconcile' the classical modelling approaches in mathematical epidemiology, based on compartmental models, with some widely used analysis results (including those by P. van den Driessche and J. Watmough in 2002), established for apparently less structured systems of nonlinear ordinary-differential equations. We take special care in explaining the modelling approach in details, and provide analysis results that allow to compute or estimate the value of the basic reproduction number for such general periodic epidemic systems.