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The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model

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  • Zhao, Yu
  • Zhang, Liping
  • Yuan, Sanling

Abstract

Media coverage is one of the important measures for controlling infectious diseases, but the effect of media coverage on diseases spreading in a stochastic environment still needs to be further investigated. Here, we present a stochastic susceptible–infected–susceptible (SIS) epidemic model incorporating media coverage and environmental fluctuations. By using Feller’s test and stochastic comparison principle, we establish the stochastic basic reproduction number R0s, which completely determines whether the disease is persistent or not in the population. If R0s≤1, the disease will go to extinction; if R0s=1, the disease will also go to extinction in probability, which has not been reported in the known literatures; and if R0s>1, the disease will be stochastically persistent. In addition, the existence of the stationary distribution of the model and its ergodicity are obtained. Numerical simulations based on real examples support the theoretical results. The interesting findings are that (i) the environmental fluctuation may significantly affect the threshold dynamical behavior of the disease and the fluctuations in different size scale population, and (ii) the media coverage plays an important role in affecting the stationary distribution of disease under a low intensity noise environment.

Suggested Citation

  • Zhao, Yu & Zhang, Liping & Yuan, Sanling, 2018. "The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 248-260.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:248-260
    DOI: 10.1016/j.physa.2018.08.113
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    3. J. Michael Harrison & Sidney I. Resnick, 1976. "The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 347-358, November.
    4. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
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    Cited by:

    1. Zhang, Xinhong & Shi, Zhenfeng & Wang, Yuanyuan, 2019. "Dynamics of a stochastic avian–human influenza epidemic model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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