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山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (1): 115-122.doi: 10.6040/j.issn.1671-9352.0.2016.117

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一类包含媒体报道的SEQIHRS传染病模型的分析

武婧媛,石瑞青*   

  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

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摘要： 研究了一类包含媒体报道与隔离措施的SEQIHRS传染病模型的动力学行为。 首先得到了系统的有效再生数RC。 其次, 通过简单计算发现:系统总是存在无病平衡点,并且当RC<1时,它是局部渐近稳定的;当RC>1时,它是不稳定的。 然后,运用中心流形定理,发现当域值RC通过1时,系统将会发生跨临界分支,并且唯一的地方病平衡点是局部渐近稳定的。 此外, 计算结果表明,被隔离个体的传染力将影响卫生部门如何实施相应的隔离措施。

关键词: 传染病模型, 稳定性, 平衡点, 媒体报道

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.

Key words: epidemic model, stability, media coverage, equilibrium

中图分类号: 

  • O175
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