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Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate

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  • Maoxing Liu
  • Yuting Chang
  • Lixia Zuo

Abstract

An epidemic model with media is proposed to describe the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that the media has its effect when the number of the infected exceeds a certain critical level. Furthermore, it is assumed that the impact of the media on the contact transmission is described by an exponential function. Stability analysis of the model shows that the disease‐free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity, a unique endemic equilibrium exists, which is also globally asymptotically stable. Our analysis implies that media coverage plays an important role in controlling the spread of the disease.

Suggested Citation

  • Maoxing Liu & Yuting Chang & Lixia Zuo, 2016. "Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:3458965
    DOI: 10.1155/2016/3458965
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    References listed on IDEAS

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    1. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yuan, Xinpeng & Xue, Yakui & Liu, Maoxing, 2013. "Analysis of an epidemic model with awareness programs by media on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 48(C), pages 1-11.
    3. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
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