Global dynamics of a stochastic avian-human influenza epidemic model with logistic growth for avian population

In this paper, a stochastic avian-human influenza epidemic model with logistic growth for avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. The dynamical behavior of this model is discussed. Firstly, the existence and uniqueness of the global positive solution are obtained. Then persistence in the mean and extinction of the infected avian population is studied. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution of stochastic avian-human influenza model are obtained. We find a threshold of this stochastic model which determines the outcome of the disease in case the white noises are small. Results show that environmental white noise is helpful for disease control. Finally, numerical simulations validate the analytical results.