具有时滞和季节性的炭疽模型的动力学分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 851-866.

具有时滞和季节性的炭疽模型的动力学分析

张太雷¹,刘俊利^2,*(),韩梦洁²

¹ 长安大学理学院西安 710064
² 西安工程大学理学院西安 700048

收稿日期:2021-08-23 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 刘俊利 E-mail:jlliu2008@126.com
基金资助:
国家自然科学基金(11801431);陕西省自然科学基础研究计划项目(2021JM-445);陕西省自然科学基础研究计划项目(2022JM-023)

Dynamics of an Anthrax Epidemiological Model with Time Delay and Seasonality

Tailei Zhang¹,Junli Liu^2,*(),Mengjie Han²

¹ School of Science, Chang'an University, Xi'an 710064
² School of Science, Xi'an Polytechnic University, Xi'an 710048

Received:2021-08-23 Online:2022-06-26 Published:2022-05-09
Contact: Junli Liu E-mail:jlliu2008@126.com
Supported by:
the NSFC(11801431);the Natural Science Basic Research Plan in Shaanxi Province(2021JM-445);the Natural Science Basic Research Plan in Shaanxi Province(2022JM-023)

摘要/Abstract

摘要：

该文建立了一个关于炭疽的时滞传染病模型，该模型考虑了炭疽传播的季节性和潜伏期.给出了模型的基本再生数 $R_{0}$ ，研究表明模型的动力学行为完全由 $R_{0}$ 来决定.当 $R_{0}$ < 1时无病周期解全局吸引，疾病绝灭；当 $R_{0}$ >1时，系统存在一个正的周期解，疾病持久生存.对相应的自治系统，根据基本再生数得到了无病平衡点和地方病平衡点的全局渐近稳定性.最后数值模拟研究了 $R_{0}$ 关于参数的敏感性及接种和尸体处理策略对炭疽传播的影响.

关键词: 炭疽, 时滞, 基本再生数, 季节性, 阈值动力学

Abstract:

In this paper, we developed a time-delayed epidemiological model to describe the anthrax transmission, which incorporates seasonality and the incubation period of the animal population. The basic reproduction number $R_{0}$ can be obtained. It is shown that the threshold dynamics is completely determined by the basic reproduction number. If $R_{0}<1$ , the disease-free periodic solution is globally attractive and the disease will die out; if $R_{0} >1$ , then there exists at least one positive periodic solution and the disease persists. We further investigate the corresponding autonomous system, the global stability of the disease-free equilibrium and the positive equilibrium is established in terms of $[R_0]$ . Numerical simulations are carried out to investigate the sensitivity of $R_0$ about the parameters, the effects of vaccination and carcass disposal on controlling the spread of anthrax is also analyzed.

Key words: Anthrax model, Time delay, Basic reproduction number, Seasonality, Threshold dynamics

中图分类号:

O175.1

张太雷,刘俊利,韩梦洁. 具有时滞和季节性的炭疽模型的动力学分析[J]. 数学物理学报, 2022, 42(3): 851-866.

Tailei Zhang,Junli Liu,Mengjie Han. Dynamics of an Anthrax Epidemiological Model with Time Delay and Seasonality[J]. Acta mathematica scientia,Series A, 2022, 42(3): 851-866.

图/表 4

图 1

系统(2.1)中染病者随时间的变化, (a) $R_0>1$ , (b) $R_0<1$ "

图 1

图 2

系统(4.1)中染病者随时间的变化, (a) $[R_0]>1$ , (b) $[R_0]<1$ "

图 2

图 3

基本再生数 $R_0$ 和 $[R_0]$ 与时滞的关系"

图 3

图 4

基本再生数 $R_0$ 与 $\varepsilon$ 和 $k$ 的关系"

图 4

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