Dynamic Behavior of a Stochastic Avian Influenza Model with Two Strains of Zoonotic Virus

Abstract

In this paper, a stochastic avian influenza model with two different pathogenic human–avian viruses is studied. The model analyzes the spread of the avian influenza virus from poultry populations to human populations in a random environment. The dynamic behavior of the stochastic avian influenza model is analyzed. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, under the condition of high pathogenic virus extinction, the persistence in the mean and extinction of the infected avian population with a low pathogenic virus is analyzed. Thirdly, the sufficient conditions for the existence and uniqueness of the ergodic stationary distribution in the stochastic avian influenza model are derived. We find the threshold of the stochastic model to determine whether the disease spreads when the white noise is small. The analysis results show that random white noise is effective for disease control. Finally, the theoretical results are verified by numerical simulation, and the numerical simulation analysis is carried out for the cases that cannot be theoretically deduced.

Keywords

• stochastic avian influenza model
• extinction
• stationary distribution