Periodic propagation of a non-autonomous reaction-diffusion host-vector epidemic model with general incidences and seasonality

Considering the complexity of host-vector diseases transmission and the phenomenon of periodic outbreaks, this paper investigates the non-autonomous and time-periodic reaction-diffusion transmission models of host-vector disease with general incidence rates and seasonality. The basic reproduction number Formula: see text and the critical wave speed Formula: see text are defined and the existence and non-existence of traveling wave solutions are studied. Specifically, when Formula: see text and Formula: see text, the existence of periodic traveling wave solutions satisfying some boundary conditions is proved by using the methods of the linear parabolic equation, the fixed point theorem and some limit techniques. The nonexistence of traveling waves is proved by using Poincaré transformation when Formula: see text for any Formula: see text or Formula: see text for any Formula: see text. Finally, the numerical simulations are given to verify the correctness of the theoretical results and to explore the spatial spread behavior.