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《Journal of Biomathematics》 2004-02
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Hepatitis Epidemic Models with Proportional and Pulse Vaccination

XU Jie ZHOU Yi-cang (Department of Mathematics, Shanghai Maritime University, Shanghai 200135 China) ( Science College, Xi'an Jiaotong University, Xi'an Shanxi 710049 China)  
Vaccination is an important strategy for the elimination of infectious diseases. Two mathematical SIR models with proportional vaccination and pulse vaccination are formulated in this paper. The dynamical behavior of these models are studied, and the basic reproductive numbers σ0 and σ1 are defined. For proportional model it is proved that the disease free equilibrium is globally asymptotically stable if σ0 1, and it is unstable if σ0 ;the endemic equilibrium is globally asymptotically stable if σ0 1. For pulse model,it is proved that the disease free periodic solution is stable if σ1 1, and it is unstable if σ1 ; the endemic periodic solution is stable if σ11 and p is sufficiently small.
【CateGory Index】: O242.1
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