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Ergodicity & dynamical aspects of a stochastic childhood disease model

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  • ur Rahman, Ghaus
  • Badshah, Qaisar
  • Agarwal, Ravi P.
  • Islam, Saeed

Abstract

The purpose of the present article is to explore dynamical aspects of a stochastic childhood diseases model. For any initial value it is shown that the Markov process of proposed model is V-geometrically ergodic. Moreover, it is found that the solutions of the underlying model are stochastically ultimately bounded and permanent for any initial conditions. Some sufficient conditions are established to show the extinction of the diseases. Also, it is shown that under some subsidiary conditions the system of stochastic differential equations is ergodic. Lastly, the effect of noise on the dynamics of model is also shown while the obtained result is illustrated graphically.

Suggested Citation

  • ur Rahman, Ghaus & Badshah, Qaisar & Agarwal, Ravi P. & Islam, Saeed, 2021. "Ergodicity & dynamical aspects of a stochastic childhood disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 738-764.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:738-764
    DOI: 10.1016/j.matcom.2020.11.015
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    References listed on IDEAS

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    1. Gibson, John, 2002. "The effect of endogeneity and measurement error bias on models of the risk of child stunting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(1), pages 179-185.
    2. Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    3. Fazal Haq & Muhammad Shahzad & Shakoor Muhammad & Hafiz Abdul Wahab & Ghaus ur Rahman, 2017. "Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-7, December.
    4. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
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