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带有非线性传染率的传染病模型 被引量：8

An epidemic model with nonlinear incidence rate
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摘要 对一类带有非线性传染率的SEIS传染病模型,找到了其基本再生数.借助动力系统极限理论,得到当基本再生数小于1时,无病平衡点是全局渐近稳定的,且疾病最终灭绝.当基本再生数大于1时,无病平衡点是不稳定的,而唯一的地方病平衡点是局部渐近稳定的.应用Fonda定理,得到当基本再生数大于1时疾病一致持续存在. For an SEIS epidemic model with nonlinear incidence rate, the basic reproduction number is found. By means of the limit theory of dynamical systems, it has been obtained that the disease-free equilibrium is globally asymptotically stable and the disease dies out eventually when the basic reproduction number is less than 1, and that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when the basic reproduction number is greater than 1. By Fonda＇s theorem, it has been obtained that the disease is uniformly persistent.
作者 辛京奇 王文娟 张凤琴 王伟
机构地区 运城学院应用数学系 空军工程大学应用数学物理系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2007年第4期391-396,共6页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 国家自然科学基金(10471040 10671209) 山西省自然科学基金(2005Z010) 山西省重点学科基金 空军工程大学理学院科研基金
关键词 传染病模型 平衡点 稳定性 持续性 epidemic model equilibrium stability persistence
分类号 O175.12 [理学—基础数学]
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参考文献10

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二级参考文献14

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同被引文献44

引证文献8

二级引证文献26

高校应用数学学报（A辑）
2007年 第4期

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