Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (4): 396-404.
李健全1,2, 张娟1, 马知恩1
LI Jian-quan1,2, ZHANG Juan1, MA Zhi-en1
摘要: An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium 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 stability of the endemic equilibrium are obtained.
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