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

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 centre. Our modelling contribution develops along two axes. To model the commuting, 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. Also, for the purposes of the study, we propose a general class of epidemiological models in which the 'force of infection' plays a central role, which extends and unifies several classes previously developed. We take special care in explaining the modelling approach in details, and provide first analytic results that allow to compute or estimate the value of the basic reproduction number for such general periodic epidemic systems.