Stationary distribution and extinction of a stochastic cattle brucellosis model

Abstract

In this paper, we propose a deterministic cattle brucellosis model and analyze the global stability of disease-free equilibrium and the persistence of the disease. Secondly, we consider environmental perturbations and present a stochastic version of the model, study the existence and uniqueness of positive solution, investigate the sufficient conditions for the existence of ergodic stationary distribution and extinction of the model. Finally, we use numerical simulation to observe the influence of the disturbance term on the original model.

Keywords

• Stochastic model
• Brucellosis
• Global stability
• Ergodic stationary distribution
• Extinction