| 一类受接种疫苗和媒体报道影响的传染病模型 |
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| 引用本文： | 曹磊,周文,张道祥.一类受接种疫苗和媒体报道影响的传染病模型[J].南通大学学报(自然科学版),2014(4):77-81. |
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| 作者姓名： | 曹磊 周文 张道祥 |
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| 作者单位： | 安徽师范大学数学计算机科学学院 |
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| 基金项目： | 国家自然科学基金项目(11302002);安徽省高校优秀青年重点项目(2011SQRLO222D) |
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| 摘 要： | 讨论一个受接种疫苗和媒体报道影响的SEIR模型,得到决定疾病是否爆发的阈值R0和RC,并应用RouthHurwitz准则分析相应的特征方程,讨论了当R01时无病平衡点是局部稳定的,当1R0≤em Ic+βIc/ρ1+μ时,地方病平衡点P1是局部渐近稳定的,当RC1时,地方病平衡点P2是局部渐近稳定的,并进一步应用Lyapunov函数讨论它们的全局稳定性.最后应用Maple进行数值模拟验证了结果,所得结果改进和扩展了文献中的相应结果.
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| 关 键 词： | SEIR疾病模型 接种疫苗 媒体 局部稳定性 全局稳定性 |
An Epidemic Model with Effected of Media and Vaccination |
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| Authors: | CAO Lei;ZHOU Wen;ZHANG Daoxiang |
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| Institution: | CAO Lei;ZHOU Wen;ZHANG Daoxiang;School of Mathematics and Computer Science, Anhui Normal University; |
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| Abstract: | Infectious disease prevention and control is still the focus of today＇s society, a SEIR epidemic model with saturated media and vaccination was investigated. The thresholds data R0 and Rc were obtained, which decide the existence of an infectious disease. By using the Routh-Hurwitz criterion to analyze the corresponding characteristic equation, when R0 〈 1 disease free equilibrium is locally asymptotically stability, when 1〈R0≤e^mIc＋βIc/ρ1＋μ the endemic equilibrium P1 is locally asymptotically stability, when Rc 〉 1, the endemic equilibrium P2 is locally asymp- totically stability, and it is global asymptotically stability after the application of Lyapunov function. The result of maple numerical simulation validated the result, which improve and extend the corresponding results in the literature. |
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| Keywords: | SEIR epidemic model vaccination media local stability global stability |
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