| 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： | 1. 山西财经大学,应用数学系,太原,030006;上海大学,数学系,上海,200436
2. 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Forda定理，研究了一类既有常数输入率又有因病死亡率的SELS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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| 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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