| 具周期性潜伏期的SEIR传染病模型的动力学 |
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| 引用本文： | 王双明,樊馨蔓,张明军,梁俊荣.具周期性潜伏期的SEIR传染病模型的动力学[J].数学物理学报(A辑),2020(2):527-539. |
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| 作者姓名： | 王双明 樊馨蔓 张明军 梁俊荣 |
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| 作者单位： | 兰州财经大学甘肃省电子商务技术与应用重点实验室;兰州财经大学信息工程学院 |
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| 基金项目： | 甘肃省科技计划(18JR3RA217);兰州财经大学科研项目(Lzufe2019B-006)。 |
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| 摘 要： | 研究了一类具有周期性潜伏期的常微分SEIR传染病模型.首先借助于染病年龄分布函数导出了模型.紧接着定义了模型的基本再生数R_0并利用耗散动力系统的相关理论证明R_0是决定疾病是否继续流行的阈值.最后,利用数值方法进一步验证了结论,并分析了忽略潜伏期的周期性对估计疾病传播能力的影响.
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| 关 键 词： | 周期性潜伏期 SEIR模型 基本再生数 持久性 |
The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period |
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| Wang Shuangming,Fan Xingman,Zhang Mingjun,Liang Junrong.The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period[J].Acta Mathematica Scientia,2020(2):527-539. |
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| Authors: | Wang Shuangming Fan Xingman Zhang Mingjun Liang Junrong |
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| Institution: | (Key Laboratory of E-Business Technology and Application of Gansu Province,Lanzhou University of Finance and Economics,Lanzhou 730020;School of Information Engineering,Lanzhou University of Finance and Economics,Lanzhou 730020) |
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| Abstract: | A SEIR ordinary differential epidemic model with time-periodic latent period is studied.Firstly,the model is derived by means of the distribution function of infected ages.Next,the basic reproduction ratio R0 is introduced,and it is shown that R0 is a threshold index for determining whether the epidemic will go extinction or become endemic using the theory of dissipative dynamic systems.Finally,numerical methods are carried out to validate the analytical results and further to invetigate the effects on evaluating the propagation of disease owning to the neglect of the periodicity of the incubation period. |
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| Keywords: | Periodic latent period SEIR model Basic Reproduction ratios Persistence |
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