| An Infectious Disease Model With Media Coverage and Limited Medical Resources北大核心CSCD |
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| 引用本文： | 刘单,王艳,任新志,刘贤宁.An Infectious Disease Model With Media Coverage and Limited Medical Resources北大核心CSCD[J].应用数学和力学,2023,44(3):333-344. |
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| 作者姓名： | 刘单 王艳 任新志 刘贤宁 |
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| 作者单位： | 西南大学 数学与统计学院，重庆 400715 |
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| 基金项目： | 国家自然科学基金(12071382；12101513；11901477)；重庆市自然科学基金(博士后基金)(cstc2021jcyj-bshX0070))；中国博士后科学基金(2021M702704) |
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| 摘 要： | 该文建立和分析了一类具有媒体报道效应和有限医疗资源的传染病动力学模型，定义了疾病的基本再生数，分析了平衡点的存在性和稳定性，给出了系统发生前向分支、后向分支和Hopf分支的条件.通过数值模拟发现：提高媒体报道的信息覆盖率或医院对病人的最大容纳量，可以显著降低疾病流行的峰值或稳态时的感染人数；随着参数变化，系统不仅可能会产生后向分支或前向分支，还可能会出现鞍结点分支、Hopf分支以及地方病平衡点稳定性随参数变化而变化等动力学行为.
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| 关 键 词： | 媒体报道 有限医疗资源 后向分支 Lyapunov稳定 |
| 收稿时间： | 2022-05-10 |
An Infectious Disease Model With Media Coverage and Limited Medical Resources |
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| Liu D.Wang Y.Ren X.Liu X..An Infectious Disease Model With Media Coverage and Limited Medical Resources[J].Applied Mathematics and Mechanics,2023,44(3):333-344. |
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| Authors: | Liu DWang YRen XLiu X |
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| Affiliation: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R.China |
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| Abstract: | A dynamical model for infectious disease with media coverage effects and limited medical resources was established and analyzed. The basic reproduction number of the disease was defined, the existence and stability of the equilibria were analyzed, and the conditions for the forward bifurcation, the backward bifurcation and the Hopf bifurcation to occur in the system were given. Numerical simulation results show that, increasing the media coverage rate or the maximum hospital capacity can significantly reduce the number of infections at the peak or in the steady state of the epidemic. With the variations of parameters, the system will exhibit dynamic behaviors including not only the backward bifurcation or the forward bifurcation, but also the saddle node bifurcation, the Hopf bifurcation, or the change of the endemic equilibrium point stability with parameters. |
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| Keywords: | backward bifurcation limited medical resources Lyapunov stability media coverage |
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