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### 一类包含媒体报道的SEQIHRS传染病模型的分析

1. 山西师范大学数学与计算机科学学院, 山西 临汾 041004
• 收稿日期:2015-03-18 出版日期:2016-01-16 发布日期:2016-11-29
• 通讯作者: 石瑞青(1979— ),男,副教授,硕士生导师,研究方向为生物数学. E-mail:shirq1979@163.com E-mail:280621185@qq.com
• 作者简介:武婧媛(1990— ),女,硕士研究生,研究方向为生态数学.E-mail:280621185@qq.com
• 基金资助:
山西省自然科学基金项目资助(2013021002-2)

### Analysis of an SEQIHRS epidemic model with media coverage

WU Jing-yuan, SHI Rui-qing*

1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, Shanxi, China
• Received:2015-03-18 Online:2016-01-16 Published:2016-11-29

Abstract: An SEQIHRS epidemic model is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies. Firstly, we obtain the effective reproduction number RC of the system. Secondly, simple calculations indicate that the system always exists a disease-free equilibrium, and it is locally asymptotically stable if RC<1, whereas it is unstable if RC>1. Thirdly, by use of central manifold theory, it is established that as RC passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. In addition, mathematical results indicate that infectiousness of hospitalized individuals will determine how the government takes control measures.

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