Analysis of an avian influenza model with Allee effect and stochasticity

In this paper, we investigate a two-dimensional avian influenza model with Allee effect and stochasticity. We first show that a unique global positive solution always exists to the stochastic system for any positive initial value. Then, under certain conditions, this solution is proved to be stochastically ultimately bounded. Furthermore, by constructing a suitable Lyapunov function, we obtain sufficient conditions for the existence of stationary distribution with ergodicity. The conditions for the extinction of infected avian population are also analytically studied. These theoretical results are conformed by computational simulations. We numerically show that the environmental noise can bring different dynamical outcomes to the stochastic model. By scanning different noise intensities, we observe that large noise can cause extinction of infected avian population, which suggests the repression of noise on the spread of avian virus.