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A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process

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  • Wang, Weiming
  • Cai, Yongli
  • Ding, Zuqin
  • Gui, Zhanji

Abstract

In this paper, based on the results of Gray et al. (2011), we propose a new SDE SIS model incorporating mean-reverting Ornstein–Uhlenbeck process, and prove that the stochastic basic reproduction number R0s can be used to identify the stochastic extinction and persistence for the SDE mode: if R0s<1 under mild extra conditions, the disease will be extinct a.s., while if R0s>1, the disease will persist a.s. Epidemiologically, we find that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak. Thus, in order to control the spread of the disease, we must decrease the speed of reversion or increase the intensity of volatility.

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  • Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:921-936
    DOI: 10.1016/j.physa.2018.06.099
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    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. 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.
    4. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    5. 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.
    6. Huo, Hai-Feng & Cui, Fang-Fang & Xiang, Hong, 2018. "Dynamics of an SAITS alcoholism model on unweighted and weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 249-262.
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