| 带有非线性传染率的传染病模型 |
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| 引用本文： | 辛京奇,王文娟,张凤琴,王伟. 带有非线性传染率的传染病模型[J]. 高校应用数学学报(A辑), 2007, 22(4): 391-396 |
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| 作者姓名： | 辛京奇 王文娟 张凤琴 王伟 |
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| 作者单位： | 1. 运城学院,应用数学系,山西运城,044000
2. 空军工程大学,应用数学物理系,陕西西安,710051 |
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| 基金项目： | 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 |
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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.
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| 关 键 词： | 传染病模型 平衡点 稳定性 持续性 |
| 文章编号： | 1000-4424（2007）04-0391-06 |
| 收稿时间： | 2007-02-15 |
| 修稿时间： | 2007-02-15 |
An epidemic model with nonlinear incidence rate |
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| XIN Jing-qi,WANG Wen-juan,ZHANG Feng-qin,WANG Wei. An epidemic model with nonlinear incidence rate[J]. Applied Mathematics A Journal of Chinese Universities, 2007, 22(4): 391-396 |
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| Authors: | XIN Jing-qi WANG Wen-juan ZHANG Feng-qin WANG Wei |
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| Abstract: | 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. |
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| Keywords: | epidemic model equilibrium stability persistence |
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