| In this paper,a dynamic model of SIS epidemic model with logistic growth and saturation treatment function was established based on the changing population characteristics and logistic growth.Based on sheep brucellosis control policies and animal testing characteristics and considering the limitation of culling resources,a dynamic model was established to study the impact of testing-culling measure on the transmission of brucellosis.The dynamic behavior of the model was studied by bifurcation theory and stability theory of ordinary differential equations.The research contents are as follows:In the second chapter,an SIS epidemic model with logistic growth and saturation treatment function was established on the changing population characteristics,and the dynamics of the model was studied.Compared with the constant population input model,the model not only occurs backward bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation,but also occurs transcritical bifurcation and pitchfork bifurcation of codimension 1.The bifurcation theory was applied to prove that the model occurs Bautin bifurcation and a cusp of codimension 2 at least.These results reveal that the dynamics of the changing population model are more complex.In the third chapter,based on sheep brucellosis control policies and animal testing characteristics and considering the limitation of culling resources,a sheep brucellosis model was established.Theoretical analysis reveals that the model may have one or three positive equilibria.The equilibrium in the middle is always unstable,and the model shows saddlenode bifurcation,generalized Hopf bifurcation and Bogdanov-Takens bifurcation.These results reveal that testing and culling strategies can induce complex transmission dynamics that can help us develop appropriate prevention and control measures.In the end,it summarizes the whole paper,clarifies the significance of the research and the factors that are not considered,and provides new ideas for further research. |
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