Heterogeneity facilitates Persistent Infection
In this paper we review some recent results obtained in our research group, on the general question of the emergence of persistent infection in a closed region (Agrawal, Moitra & Sinha (2017)). Specifically, the disease progression of the individuals is given by the SIRS model, with a susceptible individual becoming infected on contact with a neighboring infected individual. We explore the emergence of persistent infection, qualitatively and quantitatively, under increasing heterogeneity. We investigate different degrees of heterogeneity in the initial population by considering varying fractions of the initial population in different disease compartments, and by varying the spread in the phases of disease progression among the individuals. Our observation is that when the initial population is uniform, consisting of individuals at the same stage of disease progression, infection arising from a contagious seed does not persist. However when the initial population consists of randomly distributed refractory and susceptible individuals, a single source of infection can lead to sustained infection in the population, as heterogeneity facilitates the de-synchronization of the phases in the disease cycle of the individuals. We further examine the role of heterogeneity in the initial phases within the refractory compartment, and the effect it has on persistence.