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总人口规模变化的年龄结构SEIR流行病模型的稳定性
引用本文:李学志,代丽霞. 总人口规模变化的年龄结构SEIR流行病模型的稳定性[J]. 系统科学与数学, 2006, 26(3): 283-300
作者姓名:李学志  代丽霞
作者单位:1. 信阳师范学院数学系,信阳,464000
2. 空军第一航空学院,信阳,464000
基金项目:国家自然科学基金(10371105)河南省杰出青年科学基金(0312002000)资助课题.
摘    要:运用泛函分析中的谱理论和非线性发展方程的齐次动力系统理论,讨论了总人口规模变化情况下的年龄结构的SEIR流行病模型.得到了与总人口增长指数λ*有关的再生数R0的表达式,证明了当R0<1时,系统存在唯一局部渐近稳定的无病平衡态;当 R0>1时,无病平衡态不稳定,此时存在地方病平衡态,并在一定条件下证明了地方病平衡态是局部渐近稳定的.

关 键 词:年龄结构  SEIR流行病模型  齐次动力系统  再生数  平衡态  稳定性
修稿时间:2004-03-30

Stability Of An Age-Structured Seir Epidemic Model With Varying Population Size
Li Xuezhi,Dai Lixia. Stability Of An Age-Structured Seir Epidemic Model With Varying Population Size[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(3): 283-300
Authors:Li Xuezhi  Dai Lixia
Affiliation:(1)Department of Mathematics, Xinyang Teachers College, Xinyang 464000;(2)The First Aeronautic College of Air Force, Xinyang 464000
Abstract:This paper discusses an age-structured SEIR epidemic model with varying population size. By means of the spectrum theory of bounded linear operator in functional analysis and the theory of homogeneous dynamical systems in nonlinear developing equation, the reproductive number ${mathcal R}_0$, which associates with the growth rate $lambda^*$of total population size, is obtained. It is shown that there is a locally asymptoticallystable disease-free steady state if ${mathcal R}_0<1$, the disease-free steady state is unstable and there is an endemic equilibrium if ${mathcal R}_0>1$. Finally, it is proved that the endemic equilibriumis locally asymptotically stable under certain condition.
Keywords:Age-structure  SEIR epidemic model  homogenous dynamical system  reproductive number  steady states  stability  
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