An SIS epidemic model with mass action infection mechanism in a patchy environment

Abstract In this paper, we study an SIS (susceptible–infected–susceptible) epidemic model with mass action infection mechanism in a patchy environment. We first analyze the long‐time dynamics of the model in terms of the basic reproduction number , and prove under certain conditions that the disease‐free equilibrium (DFE) is globally attractive if whereas the endemic equilibrium (EE) is globally attractive if . Then we establish the existence and uniqueness of EE provided , which is achieved, among other ingredients, by reducing the equilibrium problem into the one involving only the component of infected population. We further investigate the asymptotic profile of EE as the motility rate of the susceptible and/or infected population becomes small. We also perform the theoretical analysis on the corresponding model with linear birth/death effect. By comparing the findings of the models considered here with those of other closely related ones, our results suggest that the variation of total population, individual motility, infection mechanism, and spatial heterogeneity all can play significant roles in the dynamics of disease transmission, which may shed light on the practical implications for predicting the patterns of disease outbreak and designing optimal control strategies.