Analysis of a SEIRS metapopulation model with fast migration

Abstract

Metapopulation models for the study of a infectious disease in a population with space structure involve a large number of equations. Therefore the mathematical analysis of these models yields only partial results. We propose a model in which, as it is often the case in practical situations, the time scale of the transport of individuals is much master that that of the disease. Then we make use of approximate reduction techniques in order to reduce the system’s dimension, and carry out a thorough analysis of the reduced model. In particular we characterize the number and stability of equilibria, provide conditions for the disease to become endemic (resp. die out) and show that certain counter-intuitive behaviors can arise.