一类具有非线性传染率的SEIS传染病模型的稳定性分析

邢伟; 颜七笙; 杨志辉; 高晋芳

doi:10.21656/1000-0887.370166

一类具有非线性传染率的SEIS传染病模型的稳定性分析

doi: 10.21656/1000-0887.370166

¹东华理工大学理学院, 南昌 330013;²华东交通大学理工学院, 南昌 330013

基金项目: 江西省教育厅科学技术研究项目(GJJ14469；GJJ150600);江西省高等学校教学改革研究项目(JXJG-15-6-22)

详细信息

作者简介:
邢伟(1988—), 男,硕士(通讯作者. E-mail: xingwei@ecit.cn).

中图分类号: O175.12
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- 被引次数: 0
出版历程
- 收稿日期: 2016-05-26
- 修回日期: 2016-10-09
- 刊出日期: 2016-11-15

Stability Analysis of an SEIS Epidemic ModelWith a Nonlinear Incidence Rate

¹School of Science, East China University of Technology, Nanchang 330013, P.R.China;²Institute of Technology, East China Jiaotong University,Nanchang 330013, P.R.China

摘要

摘要: 研究了一类具有非线性传染率的SEIS模型，模型中包含常数输入率、自然死亡率、因病死亡率等.定义了模型的基本再生数R₀，并证明了当R₀<1时，无病平衡点是全局渐近稳定的.当R₀＞1时，得到了唯一的地方平衡点是全局渐近稳定的条件.
- 非线性传染率 /
- SEIS模型 /
- 基本再生数 /
- 全局渐近稳定
Abstract: An SEIS epidemic model with a nonlinear incidence rate and involving a constant input rate, a natural mortality rate and a mortality rate due to disease, was investigated. Firstly, the basic reproduction number for the model was defined. Then the disease-free equilibrium point was proved to be globally asymptotically stable when R₀<1. Finally, the conditions for the theorem that the unique endemic equilibrium point was globally asymptotically stable, were obtained when R₀>1.
- nonlinear incidence rate /
- SEIS model /
- basic reproduction number /
- global asymptotic stability

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参考文献(12)

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