A periodic reaction–diffusion system modelling man–environment–man epidemics

The purpose of this work is to study the spatial dynamics of a periodic reaction–diffusion epidemic model arising from the spread of oral–faecal transmitted diseases. We first show that the disease spreading speed is coincident with the minimal wave speed for monotone periodic travelling waves. Then we obtain a threshold result on the global attractivity of either zero or the positive periodic solution in a bounded spatial domain.