Long‐Term Behavior and Extinction of a Stochastic Avian Influenza Model With Reaction–Diffusion

In this paper, the long‐term behavior and extinction of stochastic avian influenza model with reaction–diffusion are studied. For the model, on the one hand, considering the cross‐regional transmission between avian and humans, we introduce spatial diffusion. On the other hand, since the mortality rate is easily affected by external factors, we have introduced random noise on the basis of the mortality rate. Furthermore, the existence, uniqueness, positivity, and boundedness of the solution are given. Most of the previous studies have analyzed the dynamic behavior of diseases using by the basic reproduction number. In this paper, we provide the conditions for disease persistence and extinction from another perspective. Through numerical simulations, we verify the long‐term behavior and extinction of the model, which can be observed when , the infected avian population will become extinct. Therefore, when a disease outbreak occurs, we can control the development of the disease by adjusting the relevant parameters.