Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration

LI Jian-quan; ZHANG Juan; MA Zhi-en

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(4): 359-367

LI Jian-quan, ZHANG Juan, MA Zhi-en. Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration[J]. Applied Mathematics and Mechanics, 2004, 25(4): 359-367.

Citation:

LI Jian-quan, ZHANG Juan, MA Zhi-en. Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration[J]. Applied Mathematics and Mechanics, 2004, 25(4): 359-367.

Citation:

LI Jian-quan, ZHANG Juan, MA Zhi-en. Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration[J]. Applied Mathematics and Mechanics, 2004, 25(4): 359-367.

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Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration

1.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, P. R. China;

Received Date: 2002-08-05
Rev Recd Date: 2003-09-05
Publish Date: 2004-04-15

Abstract

Abstract

An epidemic models of SIR type and SIRS type with general contact rate and corntant immigration of each class were discussed by means of theory of limit system a1d suitable Iiapunov funcdons. In the absence of input of infectious individuals,the threshold of existence of endemic equifibrium is found. For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model,the suffident and necessary conditiorn of global asymptotical stabifities are all obtained For corresponding SIRS model,the sufficient conditions of global asymptotical stabilitiese of the disease-free equifibrium and the endemic equilibrium are obtained In the existence of input of infectious individuals,the models have no disease-free equilibrium. For corresponding SIR model,the endemic equilibrium is globally asymptotically stable;for corresponding SIRS model,the sufficient conditions of global asymptotical stabifitv of the endemic equilibrium are obtained.
- epidemic models,
- eqvtilibrium,
- global asymptotical stability,
- limit system

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References(8)

References

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