Threshold dynamics of a nonlocal and time-delayed West Nile virus model with seasonality

Abstract

In this paper, we study a nonlocal periodic reaction–diffusion system modeling the West Nile virus transmission between mosquitoes and birds. For the subsystem of mosquito growth, we establish a global stability result on the extinction and persistence in terms of mosquito reproduction number RM, which is defined as the cone spectral radius of a monotone homogeneous map. For the full model, we introduce the basic reproduction number R0 and show that the disease transmission dynamics is determined by the sign of R0−1 under the assumption that RM>1. Moreover, we obtain the global attractivity of the positive constant steady state in the case where all the coefficients are constants. We also conduct numerical simulations to reveal the effects of diffusion, heterogeneity and periodic delay on R0.