An SEI infection model incorporating media impact

1.
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2.
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China
3.
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA

Received: 08 July 2016 Published: 01 October 2017
MSC : Primary: 34A34, 92C50, 92C60

Abstract
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To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number $\Re_0$ for the model, and show that the modeled disease dies out regardless of initial infections when $\Re_0 \lt 1$, and becomes uniformly persistently endemic if $\Re_0 \gt 1$. When the disease is endemic and the influence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided $\Re_0 $ is greater than and near one. However, if $\Re_0 $ is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the influence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger $\Re_0$, the influence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases.
- Media impact,
- Hopf bifurcation,
- stability,
- infectious disease
Citation: Xuejuan Lu, Shaokai Wang, Shengqiang Liu, Jia Li. An SEI infection model incorporating media impact[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1317-1335. doi: 10.3934/mbe.2017068

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Abstract

To study the impact of media coverage on spread and control of infectious diseases, we use a susceptible-exposed-infective (SEI) model, including individuals' behavior changes in their contacts due to the influences of media coverage, and fully investigate the model dynamics. We define the basic reproductive number $\Re_0$ for the model, and show that the modeled disease dies out regardless of initial infections when $\Re_0 \lt 1$, and becomes uniformly persistently endemic if $\Re_0 \gt 1$. When the disease is endemic and the influence of the media coverage is less than or equal to a critical number, there exists a unique endemic equilibrium which is asymptotical stable provided $\Re_0 $ is greater than and near one. However, if $\Re_0 $ is larger than a critical number, the model can undergo Hopf bifurcation such that multiple endemic equilibria are bifurcated from the unique endemic equilibrium as the influence of the media coverage is increased to a threshold value. Using numerical simulations we obtain results on the effects of media coverage on the endemic that the media coverage may decrease the peak value of the infectives or the average number of the infectives in different cases. We show, however, that given larger $\Re_0$, the influence of the media coverage may as well result in increasing the average number of the infectives, which brings challenges to the control and prevention of infectious diseases.

References

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