Noise-induced transitions in an avian influenza model with the Allee effect

Abstract

Abstract This paper presents noise-induced transitions in a stochastic avian influenza model with Allee effect. In the deterministic case, one of three disease-free equilibria is always globally asymptotically stable in its attractive domain, and there is a unique endemic equilibrium when the basic reproduction number R 0 > 1 $R_{0}>1$ . In the stochastic case, a new dynamic phenomenon of noise-induced transition can be observed, that is, the stochastic trajectory can exit from the neighborhood of the epidemic equilibrium and pass into the vicinity of the trivial equilibrium. More precisely, in this paper, based on the stochastic sensitivity function technique, we construct the confidence ellipse and then estimate the critical value of the noise intensity leading to extinction. We also propose useful control strategies to prevent the noise-induced extinction.

Keywords

• Stochastic avian influenza model
• Allee effect
• Noise-induced transition
• Stochastic sensitivity