基于总人口变动和隔离措施的SIQS传染病模型的渐近分析

doi:10.3969/j.issn.0253-2778.2020.03.004

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (3): 282-288.DOI: 10.3969/j.issn.0253-2778.2020.03.004

基于总人口变动和隔离措施的SIQS传染病模型的渐近分析

傅金波

福建师范大学闽南科技学院

收稿日期:2019-01-17 修回日期:2020-05-22 接受日期:2020-05-22 出版日期:2020-03-31 发布日期:2020-05-22
作者简介:傅金波，男，1978年生，硕士/教授. 研究方向：生物数学. E-mail: fujinbomnkjxy@sina.com
基金资助:
国家自然科学基金(11371306)，福建省高等学校新世纪人才支持计划，泉州市科技计划(2018C094R)资助.

Asymptotic analysis of an SIQS epidemic model with varying total population size and quarantine measures

FU Jingbo

Minnan Science and Technology University, Quanzhou 362332, China

Received:2019-01-17 Revised:2020-05-22 Accepted:2020-05-22 Online:2020-03-31 Published:2020-05-22

摘要/Abstract

摘要： 根据传染病动力学原理，考虑人口既有输入又有输出,建立了一种具有总人口变动和隔离措施及垂直传染的SIQS传染病模型.综合利用Routh-Hurwitz判据，Lyapunov函数和广义Bendixson-Dulac函数方法，获得了该系统的无病平衡点和地方病平衡点全局渐近稳定的充分条件.研究结果表明：采取隔离措施，能够将疾病的传播和流行控制在一定范围内，甚至能够加快疾病的绝灭.

关键词: SIQS传染病模型, 隔离措施, 垂直传染, 全局渐近稳定性

Abstract: A class of SIQS epidemic model with vertical infection and varying total population size and quarantine measures was established, by employing the epidemic dynamic theory, and considering both the input and output of the population. The threshold conditions which guarantee the global asymptotic stable disease-free equilibrium and endemic equilibrium of the SIQS epidemic model are obtained using methods including Routh-Hurwitz bounded, Lyapunov function and generalized Bendixson-Dulac function. The results show that the spread and prevalence of a disease can be controlled within a certain range, and that quarantine measures can accelerate the extinction of the disease.

Key words: SIQS epidemic model, Quarantine measures, Vertical infection, Global asymptotic stability

中图分类号:

O175.1

傅金波. 基于总人口变动和隔离措施的SIQS传染病模型的渐近分析[J]. 中国科学技术大学学报, 2020, 50(3): 282-288.

FU Jingbo. Asymptotic analysis of an SIQS epidemic model with varying total population size and quarantine measures[J]. Journal of University of Science and Technology of China, 2020, 50(3): 282-288.

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基于总人口变动和隔离措施的SIQS传染病模型的渐近分析

Asymptotic analysis of an SIQS epidemic model with varying total population size and quarantine measures

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