具周期性潜伏期的SEIR传染病模型的动力学

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 527-539.

具周期性潜伏期的SEIR传染病模型的动力学

王双明^1,^2,*(),樊馨蔓²,张明军²,梁俊荣²

¹ 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 730020
² 兰州财经大学信息工程学院兰州 730020

收稿日期:2018-11-14 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 王双明 E-mail:wsm@lzufe.edu.cn
基金资助:
甘肃省科技计划(18JR3RA217);兰州财经大学科研项目(Lzufe2019B-006)

The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period

Shuangming Wang^1,^2,*(),Xingman Fan²,Mingjun Zhang²,Junrong Liang²

¹ Key Laboratory of E-Business Technology and Application of Gansu Province, Lanzhou University of Finance and Economics, Lanzhou 730020
² School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020

Received:2018-11-14 Online:2020-04-26 Published:2020-05-21
Contact: Shuangming Wang E-mail:wsm@lzufe.edu.cn
Supported by:
the Science and Technology Planed Projects of Gansu Province(18JR3RA217);the Research Project of Lanzhou University of Finance and Economics(Lzufe2019B-006)

摘要/Abstract

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$\mathcal R_0$并利用耗散动力系统的相关理论证明$\mathcal R_0$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.

关键词: 周期性潜伏期, SEIR模型, 基本再生数, 持久性

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 $\mathcal R_0$ is introduced, and it is shown that $\mathcal R_0$ 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.

Key words: Periodic latent period, SEIR model, Basic Reproduction ratios, Persistence

中图分类号:

O175

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, 2020, 40(2): 527-539.

Shuangming Wang,Xingman Fan,Mingjun Zhang,Junrong Liang. The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period[J]. Acta mathematica scientia,Series A, 2020, 40(2): 527-539.

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