Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment

In this paper, we propose a mathematical model to describe the avianinfluenza dynamics in wild birds with bird mobility andheterogeneous environment incorporated. In addition to establishingthe basic properties of solutions to the model, we also prove thethreshold dynamics which can be expressed either by the basicreproductive number or by the principal eigenvalue of thelinearization at the disease free equilibrium. When the environmentfactor in the model becomes a constant (homogeneous environment), weare able to find explicit formulas for the basic reproductivenumber and the principal eigenvalue. We also perform numericalsimulation to explore the impact of the heterogeneous environment onthe disease dynamics. Our analytical and numerical results revealthat the avian influenza dynamics in wild birds is highly affectedby both bird mobility and environmental heterogeneity.