一类具有饱和传染率的SVEIR传染病模型的定性分析

建立带有接种的SVEIR传染病模型,得到基本再生数R_0,并讨论平衡点的存在性.通过构造Lyapunov函数及利用LaSalle不变原理,研究连续接种对传染病传播的影响.发现传染病模型的全局稳定性由基本再生数R0决定,当R0〈1时,无病平衡点全局渐近稳定.当R0〉1时,地方病平衡点全局渐近稳定.接种是控制疾病传播的有效途径....

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Bibliographic Details
Published in西安工程大学学报 Vol. 31; no. 5; pp. 706 - 712
Main Author 吴梦媛;孙法国;陈瑶
Format Journal Article
LanguageChinese
Published 西安工程大学 理学院,陕西 西安,710048 2017
Subjects
全局稳定性
基本再生数
连续接种
饱和发生率
饱和发生率
continuous vaccination
全局稳定性
saturation incidence rate
连续接种
global stability
基本再生数
basic reproduction number
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Summary:建立带有接种的SVEIR传染病模型,得到基本再生数R_0,并讨论平衡点的存在性.通过构造Lyapunov函数及利用LaSalle不变原理,研究连续接种对传染病传播的影响.发现传染病模型的全局稳定性由基本再生数R0决定,当R0〈1时,无病平衡点全局渐近稳定.当R0〉1时,地方病平衡点全局渐近稳定.接种是控制疾病传播的有效途径.
Bibliography:WU Mengyuan ,SUN Faguo ,CHEN Yao （School of Science,Xi＇an Polytechnic University,Xi＇an710048,China）
continuous vaccination;saturation incidence rate;basic reproduction number;global stability
61-1471/N
The SVEIR infectious disease model with vaccination is established,the basic repro-duction number is obtained,and the existence of the equilibrium point is discussed.The effects of continuous vaccination on infectious diseases by constructing Lyapunov function and the La-Salle＇s invariance principle.It is pointed out that the basic reproduction number R 0 determines the global stability of the epidemic model.When R 0〈1,the disease-free equilibrium is globally asymptotically stable.When R 0〉 1,the endemic equilibrium is globally asymptotically stable. The results show that continuous vaccination is an effective way to control the disease.
ISSN:1674-649X
DOI:10.13338/j.issn.1674-649x.2017.05.018