| 一类受媒体影响的传染病模型的研究 |
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| 引用本文： | 刘玉英,肖燕妮.一类受媒体影响的传染病模型的研究[J].应用数学和力学,2013,34(4):399-407. |
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| 作者姓名： | 刘玉英 肖燕妮 |
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| 作者单位： | 西安交通大学 数学与统计学院,西安 710049 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 媒体报道对传染病的感染率有着重要的影响，为探究这种影响建立了一个受媒体影响且具有分段感染率的传染病模型．首先，计算出模型的所有平衡态，并根据基本再生数的大小分析了各平衡态的局部稳定性．其次，通过排除极限换的存在性证明了平衡态的全局渐近稳定性．最后，对媒体影响传染病模型的动力学性态进行了讨论．
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| 关 键 词： | 媒体影响 传染病模型 分段光滑 全局渐近稳定性 |
| 收稿时间： | 2013-03-10 |
An Epidemic Model With Saturated Media/Psychological Impact |
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| Institution: | Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an 710049, P.R.China |
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| Abstract: | Media has important influence on incidence rate of infectious disease. An epidemic model with segmented incidence rate was formulated and analyzed to describe the saturated media/psychology impact. Firstly all possible regular/virtual equilibria of the system was found out, and the local stability of the equilibria was analyzed in terms of the basic reproduction number. The global asymptotic stability of the positive equilibriums could then be obtained by excluding the existence of limit cycle for the system. The effect of saturated media/psychology impact on dynamics was discussed. |
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