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Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View

Author

Listed:
  • Shah Hussain

    (Faculty of Informatics and Computing, Besut Campus, Universiti Sultan Zainal Abidin (UniSZA), Besut 22200, Terengganu, Malaysia
    These authors contributed equally to this work.)

  • Elissa Nadia Madi

    (Faculty of Informatics and Computing, Besut Campus, Universiti Sultan Zainal Abidin (UniSZA), Besut 22200, Terengganu, Malaysia
    These authors contributed equally to this work.)

  • Hasib Khan

    (Department of Mathematics, Shaheed Benazir Bhutto Univeresity, Dir Upper, Sheringal 18050, Khyber Pakhtunkhwa, Pakistan
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    These authors contributed equally to this work.)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

  • Nichaphat Patanarapeelert

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

Abstract

In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R 0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ 1 , σ 2 and β 1 , β 2 , and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.

Suggested Citation

  • Shah Hussain & Elissa Nadia Madi & Hasib Khan & Sina Etemad & Shahram Rezapour & Thanin Sitthiwirattham & Nichaphat Patanarapeelert, 2021. "Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View," Mathematics, MDPI, vol. 9(23), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3122-:d:694464
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    References listed on IDEAS

    as
    1. Sweilam, N.H. & AL - Mekhlafi, S.M. & Baleanu, D., 2021. "A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Shah, Kamal & Alqudah, Manar A. & Jarad, Fahd & Abdeljawad, Thabet, 2020. "Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Babaei, A. & Jafari, H. & Banihashemi, S. & Ahmadi, M., 2021. "Mathematical analysis of a stochastic model for spread of Coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    Cited by:

    1. Publio Darío Cortés-Carvajal & Mitzi Cubilla-Montilla & David Ricardo González-Cortés, 2022. "Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(2), pages 1-30, January.

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