Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration
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摘要: 借助极限系统理论和构造适当的Liapunov函数，对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时，地方病平衡点存在的阈值被找到A·D2对相应的SIR模型，关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型，得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时，模型不存在无病平衡点．对相应的SIR模型，地方病平衡点是全局渐近稳定的；对相应的SIRS模型，得到地方病平衡点全局渐近稳定的充分条件．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.
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Key words:
- epidemic models /
- eqvtilibrium /
- global asymptotical stability /
- limit system
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[1] Kermack W O,McKendrick A G.Contributions to the mathematical theory of epidemics—Part 1[J].Proc Roy Soc London Ser A,1927,115(3):700—721. doi: 10.1098/rspa.1927.0118 [2] Mena-Lorca J,Hethcote H W.Dynamic models of infectious diseases as regulators of population sizes[J].J Math Biol,1992,30(4):693—716. [3] Li J,Ma Z.Qualitative analysis of SIS epidemic model with vaccination and varying total population size[J].Math Comput Modelling,2002,35(11/12):1235—1243. doi: 10.1016/S0895-7177(02)00082-1 [4] Heesterbeck J A P,Metz J A J.The saturating contact rate in marriage-and epidemic models[J].J Math Biol,1993,31(2):529—539. [5] Brauer F,Van den Driessche P.Models for transmission of disease with immigration of infectives[J].Math Biosci,2001,171(2):143—154. doi: 10.1016/S0025-5564(01)00057-8 [6] Han L,Ma Z,Hethcote H W.Four predator prey models with infectious diseases[J].Math Comput Modelling,2001,34(7/8):849—858. doi: 10.1016/S0895-7177(01)00104-2 [7] LaSalle J P.The Stability of Dynamical System[M].New York:Academic Press,1976. [8] Jeffries C,Klee V,Van den Driessche P.When is a matrix sign stable?[J].Canad J Math,1977,29(2):315—326. doi: 10.4153/CJM-1977-035-3 -
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