LAUSR

Abstract In this paper, we propose an SIRS influenza model with general incidence rate to describe disease transmission in a heterogenous environment. The basic reproduction number R 0 is defined for the model, which can be used to govern the threshold dynamics of influenza disease: if R 0 1 , the unique disease-free equilibrium is globally asymptotic stable and there is no endemic equilibrium, while R 0 > 1 , there is at least one endemic equilibrium and the disease is uniformly persistent. Epidemiologically, we find that the spatial heterogeneity can enhance the infectious risk of the influenza and thus, in order to control the spread of the influenza, we must increase the recovery rate and the spatial heterogeneity in the transmission rate, or people should change their travelling plan and stay at home to reduce the value of the diffusion coefficient.