LONG-TIME BEHAVIOR OF AVIAN INFLUENZA MODEL WITH NONLOCAL DIFFUSION

The aim of this study is to investigate the long-time behavior of a model of avian influenza incorporating nonlocal diffusion. We establish the existence, uniqueness, positivity and boundedness of the solution by constructing a Lyapunov function and utilizing the eigenvalue problem of the nonlocal diffusion term. The basic reproduction number is determined through the generation matrix method. By constructing Lyapunov function and using the comparison principle, we demonstrate the global stability and uniform persistence of the system. Numerical simulations are performed to validate our theoretical findings, indicating that diffusion has a pronounced impact on the disease. Our findings reveal that slight changes in the diffusion coefficient lead to significant changes in both susceptible and infected groups. Therefore, to control the development and spread of the disease, it is essential to cull avian populations and limit human movement during outbreaks.