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The Stability for a Class of Epidemic Model with Population Change

ZHANG Hui(School of Sciences,Nantong University,Nantong 226007,China)  
An epidemic dynamic model is analyzed considering population′s constant input and index death and the death caused by diseases.Through constructing the Dulac and Liapunov functions,and using the LaSalle invariant set theorem and the theory of limit systems,a threshold θ which determines the existence of the infectious disease is derived.The equilibrium points and their stability are found and analyzed.The result indicates when θ≥1,there only exists disease-free equilibrium point E0,which is globally asymptotically stable while θ1.When θ1,there exist two equilibrium points,the disease-free equilibrium point E0 and endemic equilibrium point E+,in which the E0 is unstable and the E+ is globally asymptotically stable.
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