Dynamics of a stochastic multi-stage sheep brucellosis model with incomplete immunity

Abstract

This paper considered a multi-stage sheep brucellosis model with incomplete immunity. First, we established a deterministic model, calculated the basic reproduction number [Formula: see text], set out the conditions for the global stability of the disease-free equilibrium and endemic equilibrium. Second, considering the influence of environmental white noise on brucellosis infection, we further established the stochastic version of the model. By constructing a suitable Lyapunov function, we proved the existence and uniqueness of the global positive solution. Further, we got the sufficient conditions for disease extinction and the existence of ergodic stationary distribution. Finally, we carried out some numerical simulations to verify the theoretical results.