Global stability for a sheep brucellosis model with immigration

Sheep brucellosis is one of the major infectious and contagious bacterial diseases in the sheep farms of China. In this paper, we present a sheep brucellosis model with immigration and proportional birth, and consider both direct and indirect transmission with infected animals and the bacteria of the environment. The basic reproduction number R0R0 of this model is identified and global dynamics are completely determined by R0R0. If R0<1R0<1, the disease-free equilibrium is global asymptotically stable; whereas if R0>1R0>1, there is a unique endemic equilibrium which is global asymptotically stable. By numerical simulations for the cases with R0<1R0<1 and R0>1R0>1 to demonstrate the global stability of the disease-free equilibrium and the unique endemic equilibrium, respectively. In addition, sensitivity analysis of the basic reproduction number in term of some parameters is given, this paper confirmed that elimination, vaccination and disinfection are the useful control strategies, and proposed to reduce immigration and self-sufficiency of the flock for controlling sheep brucellosis.