| 一类带有非线性传染率的SEIS传染病模型的定性分析 |
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| 引用本文： | 王拉娣,李建全. 一类带有非线性传染率的SEIS传染病模型的定性分析[J]. 应用数学和力学, 2006, 27(5): 591-596 |
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| 作者姓名： | 王拉娣 李建全 |
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| 作者单位： | 山西财经大学 应用数学系,太原 030006;2.上海大学 数学系, 上海 200436;3.空军工程大学 应用数学物理系,西安 710051 |
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| 摘 要： | 借助极限理论和Fonda定理,研究了一类既有常数输入率又有因病死亡率的SEIS传染病模型．所考虑模型的传染率是非线性的,并且得到了该模型的基本再生数，当基本再生数小于1时,该模型仅存在唯一的无病平衡点,它是全局渐近稳定的,且疾病最终灭绝．当基本再生数大于1时,该模型除存在不稳定的无病平衡点外,还存在唯一的局部渐近稳定的地方病平衡点,并且疾病一致持续存在．
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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： | 1000-0887（2006）05-0591-06 |
| 收稿时间： | 2004-07-31 |
| 修稿时间： | 2006-02-10 |
Qualitative Analysis of an SEIS Epidemic Model With Nonlinear Incidence Rate |
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| WANG La-di,LI Jian-quan. Qualitative Analysis of an SEIS Epidemic Model With Nonlinear Incidence Rate[J]. Applied Mathematics and Mechanics, 2006, 27(5): 591-596 |
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| Authors: | WANG La-di LI Jian-quan |
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| Affiliation: | Department of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P. R. China; |
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| Abstract: | By means of limit theory and Fonda's theorem,an SEIS epidemic model with constant recruitment and the disease-related rate is considered.The incidence term is of the nonlinear form,and the basic reproduction number was found.If the basic reproduction number is less than one,there exists only the disease-free equilibrium which is globally asymptotically stable,and the disease dies out eventually.If the basic reproduction number is greater than one,besides the unstable disease-free equilibrium,there exists also a unique endemic equilibrium,which is locally asymptotically stable,and the disease is uniformly persistent. |
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| Keywords: | epidemic models equilibrium stability persistence |
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