Dynamic analysis of sheep Brucellosis model with environmental infection pathways.

We develop a mathematical model for the transmission of brucellosis in sheep taking into account external inputs, immunity, stage structure and other factors. We find the the basic reproduction number $ R_0 $ in terms of the model parameters, and prove the global stability of the disease-free equilibrium. Then, the existence and global stability of the endemic equilibrium is proven. Finally, sheep data from Yulin, China are employed to fit the model parameters for three different environmental infection exposure conditions. The variability between different models in terms of control measures are analyzed numerically. Results show that the model is sensitive to the control parameters for different environmental infection exposure functions. This means that in practical modeling, the selection of environmental infection exposure functions needs to be properly considered.