Propagation dynamics of cooperative reaction-diffusion systems in a periodic shifting environment

Abstract

This paper is devoted to the study of propagation dynamics for a large class of nonautonomous cooperative reaction-diffusion systems in a time-periodic shifting environment. We first establish the spreading properties of solutions and the existence of forced time-periodic waves for such a system by appealing to the abstract theory developed for monotone semiflows with asymptotic translation invariance. Then we prove the uniqueness of the forced wave and its attractivity under appropriate conditions. Finally, we apply our analytical results to a reaction-diffusion-advection model of malaria transmission.