Travelling waves and global attractivity of an SIRS disease model with spatial diffusion and temporary immunity

An SIRS disease model with saturation incidence rate, time delay and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of an endemic steady state and a disease-free steady state is discussed. By comparison arguments, if the basic reproductive number is greater than unity, sufficient conditions are obtained for the global attractivity of the endemic steady state. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder’s fixed point theorem.