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Qualitative Analysis of Epidemic Models with Vaccination and Isolation

LI Dong-mei,LIU Wei-hua,ZHENG Zhong-tao(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China)  
This paper studies infectious disease model with Vaccination and isolation.The threshold which determines the spread of the disease is found.The judgement conditions of the disease-free equilibrium point and the endemic equilibrium point is given.Using LaSalle Invariant theory,the global asymptotical stability of the disease-free point is proved.Using Hurwitz criterion,the sufficient condition for the local stability of the endemic equilibrium point is obtained.The application of the method of flow uniform persistence P0k k+d,discusses the uniform persistence of solutions.Using compound matrix,the sufficient conditions for the global asymptotic stability of the endemic equilibrium is obtained.
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