Role of seasonality and spatial heterogeneous in the transmission dynamics of avian influenza

In this paper, we propose a time-periodic reaction–diffusion model with environment transmission and spatial heterogeneity to describe the transmission of avian influenza virus between birds, poultry and human population. Firstly, we study the well-posedness of solutions, including the existence and boundedness of global solutions and the existence of the global attractor of solution semiflow. Then, the basic reproduction number R0 of the model is defined, and we prove R0 is a threshold determining the global dynamics of the model. Furthermore, we analyze the dynamic behavior of the autonomous reaction–diffusion model, and obtain the existence and global attractivity of endemic equilibrium. Finally, we give some numerical examples and simulations to illustrate the main theoretical results and investigate the impacts of some model parameters on R0.