Abstract
In this paper, based on characteristics of brucellosis infection in some regions in China, a multi-stage dynamic model is proposed for sheep brucellosis transmission. The birth rate is related to the adult and vaccinated sheep. More realistically, the immigration from other place is also considered. Firstly, the basic reproduction number $ R_{0}$ is determined and the dynamical properties of the model is discussed. It is concluded that the unique endemic equilibrium exists when $ R_{0}>1$. By constructing suitable Lyapunov function, the global stability of the endemic equilibrium is verified. By carrying out sensitivity analysis of the basic reproduction number in term of the parameters, it is concluded that increasing the sheep vaccination rate and elimination rate of infected sheep is important for the control brucellosis.
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