A delayed SIQR epidemic model with media effect and tracking quarantine

doi:10.3785/j.issn.1008-9497.2022.02.004

Journal of Zhejiang University (Science Edition)

2022, Vol. 49

Issue (2): 159-169 DOI: 10.3785/j.issn.1008-9497.2022.02.004

Mathematics and Computer Science

A delayed SIQR epidemic model with media effect and tracking quarantine

Yuqian ZHANG(

),Tailei ZHANG(

),Wenshan HOU,Xueli SONG

School of Science，Chang'an University，Xi'an 710064，China

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Abstract

In this paper, a delayed SIQR epidemic model with media effect and tracking quarantine is established, the basic reproduction number $R 0$ of the model is given. The model is analyzed theoretically and simulated numerically from the perspective of stability, persistence and bifurcation. The results show that Hopf bifurcations occur when the delay $τ$ generated by media reports passes through a sequence of critical values. When $τ$ is fixed, As the degree of deviation $δ$ of susceptible persons' understanding of disease information under media reports increases continuously, the model will change from periodic oscillation to equilibrium point. With the increase of $β 0$ and $β 00$ , the maximum reduction effect of media reports on the effective contact rate, the model will change from equilibrium to periodic oscillation. Finally, the influence of different $δ$ , $β 0$ , $β 00$ and $δ$ which denotes the accuracy of media reports on the relevant information of the quarantined persons on the development of infectious diseases is studied. The results suggest that it is beneficial for the media to widely report the information of infectious diseases and improve the information accuracy so as to reduce the spread of infectious diseases and effectively control the outbreak of infectious diseases.

Key words： media coverage tracking isolation a delayed SIQR epidemic model stability Hopf bifurcation

Received: 08 June 2021 Published: 22 March 2022

CLC:

O 175

Corresponding Authors: Tailei ZHANG E-mail: yuqianzhang2020@126.com;tlzhang@chd.edu.cn

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Cite this article:

Yuqian ZHANG,Tailei ZHANG,Wenshan HOU,Xueli SONG. A delayed SIQR epidemic model with media effect and tracking quarantine. Journal of Zhejiang University (Science Edition), 2022, 49(2): 159-169.

URL:

https://www.zjujournals.com/sci/EN/Y2022/V49/I2/159

一类具有媒体效应和追踪隔离的SIQR时滞传染病模型

建立了一类具有媒体效应和追踪隔离的SIQR时滞传染病模型，给出了模型的基本再生数 $R 0$ ，并从稳定性、持久性和分支角度对该模型进行了理论分析和数值模拟。研究结果表明，由媒体报道产生的时滞 $τ$ 在各影响因子的临界值处出现Hopf分支。当 $τ$ 固定时，随着媒体的广泛报道，易感者对疾病信息认识的偏差程度 $δ$ 不断增加，模型由周期性振荡转为平衡；随着有效接触率最大削减作用 $β 0$ 和 $β 00$ 的不断增加，模型又由平衡状态转为周期性振荡。还研究了 $δ$ ， $β 0$ ， $β 00$ 以及被追踪隔离者相关信息的媒体报道准确率 $σ$ 对传染病发展的影响。结果表明，媒体对传染病信息的广泛报道以及提高报道信息的准确率可降低疾病传播，有利于控制传染病。

关键词： 媒体报道, 追踪隔离, SIQR时滞模型, 稳定性, Hopf分支

Fig.1 Compartment diagram of model 1

Fig.2 The endemic equilibrium

E * = (1.683 0,0.210 8)

is locally asymptotically stable when

τ = 10.5

Fig.3 Phase diagram of local asymptotically stable

E *

when

τ = 10.5

Fig.4 The branching periodic solution of system （2） appears when

τ = 12.5

Fig.5 Phase diagram of

E *

when

τ = 12.5

Fig.6 Branching diagram of susceptible

τ

and infected persons relative to in system （2）

Fig.7 Branching diagram of susceptible

δ

and infected persons relative to in system （2）

Fig.8 Branching diagram of susceptible and infected persons relative to

β 0

and

β 00

in system （2）

Fig.9 The influence of parameter

β 0

I (t)

Fig.10 The influence of parameter

β 00

I (t)

Fig.11 The influence of parameter

δ

I (t)

Fig.12 The influence of parameter

σ

I (t)


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