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SDE SIS epidemic model with demographic stochasticity and varying population size

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  • Greenhalgh, D.
  • Liang, Y.
  • Mao, X.

Abstract

In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.

Suggested Citation

  • Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "SDE SIS epidemic model with demographic stochasticity and varying population size," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 218-238.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:218-238
    DOI: 10.1016/j.amc.2015.11.094
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    3. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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    Cited by:

    1. Wei, Wei & Xu, Wei & Song, Yi & Liu, Jiankang, 2021. "Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Nian, Fuzhong & Yao, Shuanglong, 2018. "The epidemic spreading on the multi-relationships network," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 866-873.
    3. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    4. Guo, Xiaoxia & Luo, Jiaowan, 2018. "Stationary distribution and extinction of SIR model with nonlinear incident rate under Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 471-481.

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