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Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory

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  • Hussain, Shah
  • Tunç, Osman
  • Rahman, Ghaus ur
  • Khan, Hasib
  • Nadia, Elissa

Abstract

The “Middle East Respiratory” (MERS-Cov) is among the world’s dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration.

Suggested Citation

  • Hussain, Shah & Tunç, Osman & Rahman, Ghaus ur & Khan, Hasib & Nadia, Elissa, 2023. "Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 130-150.
    • Handle: RePEc:eee:matcom:v:207:y:2023:i:c:p:130-150
    DOI: 10.1016/j.matcom.2022.12.023
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    References listed on IDEAS

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    1. Begum, Razia & Tunç, Osman & Khan, Hasib & Gulzar, Haseena & Khan, Aziz, 2021. "A fractional order Zika virus model with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Zhi-Qiang Xia & Juan Zhang & Ya-Kui Xue & Gui-Quan Sun & Zhen Jin, 2015. "Modeling the Transmission of Middle East Respirator Syndrome Corona Virus in the Republic of Korea," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-13, December.
    4. Qixing Han & Daqing Jiang & Chengjun Yuan, 2013. "Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
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    Cited by:

    1. Muhammad Shoaib Arif & Kamaleldin Abodayeh & Yasir Nawaz, 2023. "A Computational Scheme for Stochastic Non-Newtonian Mixed Convection Nanofluid Flow over Oscillatory Sheet," Energies, MDPI, vol. 16(5), pages 1-17, February.
    2. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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