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| 总人口规模变化的年龄结构MSEIR流行病模型的再生数 | |
| 引用本文： | 李学志,万志超,陈清江.总人口规模变化的年龄结构MSEIR流行病模型的再生数[J].数学的实践与认识,2005,35(8):113-122. |
| 作者姓名： | 李学志 万志超 陈清江 |
| 作者单位： | 1. 信阳师范学院数学系,河南,信阳,464000 2. 漯河医学高等专科学校,河南,漯河,462000 3. 西安交通大学理学院,陕西,西安,710049 |
| 基金项目： | 国家自然科学基金(10371105)，河南省自然科学基金(0312002000，0211044800)资助 |
| 摘 要： | 在总人口规模变化和疾病影响死亡率的假设下,讨论了带二次感染和接种疫苗的年龄结构MSEIR流行病模型.首先给出再生数R(ψ,λ)(这里ψ(a)是接种疫苗率,λ是总人口的增长指数)的显式表达式.其次,证明了当R(ψ,λ)<1时,系统的无病平衡态是稳定的;当R(ψ,λ)>1时,无病平衡态是不稳定的. |
| 关 键 词： | 年龄结构 MSEIR流行病模型 再生数 平衡态 稳定性 |
| 修稿时间： | 2003年12月30 |
The Reproductive Number of Age-Structured MSEIR Epidemic Model with Varying Total Population Size |
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| LI Xue-zhi,WAN Zhi-chao,CHEN Qing-jiang.The Reproductive Number of Age-Structured MSEIR Epidemic Model with Varying Total Population Size[J].Mathematics in Practice and Theory,2005,35(8):113-122. | |
| Authors: | LI Xue-zhi WAN Zhi-chao CHEN Qing-jiang |
| Institution: | LI Xue-zhi 1,WAN Zhi-chao 2,CHEN Qing-jiang 3 |
| Abstract: | We discuss an age-structured MSEIR epidemic model with the loss of immunity and an age-dependent vaccination rate ψ(a)under the assumption of varying total population size and death-rate dependent of some diseases. First, we obtain an explicit formula for the reproductive number R(ψ, )where ψ(a)is the vaccination rate and is the growth exponent of total population. Next, we prove that the disease-free steady state is linearly stable if R(ψ, )is less than one and unstable if R(ψ, )is larger than one. Finally, we obtain formula for the critical reproductive numer under the assumption of constant-sized population as a special case. |
| Keywords: | age-structure MSEIR epidemic model reproductive number disease-free steady state stability |
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