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Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference

Author

Listed:
  • Xuan Leng

    (School of Science, Hunan City University, Yiyang 413000, China)

  • Asad Khan

    (School of Computer Science and Cyber Engineering, Guangzhou University, Guangzhou 510006, China)

  • Anwarud Din

    (Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China)

Abstract

When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that R s 0 > 1 , and it was noticed that, for R s < 1 , the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular.

Suggested Citation

  • Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1806-:d:1120436
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    References listed on IDEAS

    as
    1. Peijiang Liu & Mati ur Rahman & Anwarud Din, 2022. "Fractal fractional based transmission dynamics of COVID-19 epidemic model," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 25(16), pages 1852-1869, December.
    2. Omame, Andrew & Abbas, Mujahid & Din, Anwarud, 2023. "Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 302-336.
    3. Saima Rashid & Aasma Khalid & Yeliz Karaca & Yu-Ming Chu, 2022. "Revisiting Fejã‰R–Hermite–Hadamard Type Inequalities In Fractal Domain And Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-26, August.
    4. Amar Nath Chatterjee & Fahad Al Basir & Bashir Ahmad & Ahmed Alsaedi, 2022. "A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    5. Din, Anwarud & Li, Yongjin & Khan, Tahir & Zaman, Gul, 2020. "Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Din, Anwarud & Khan, Amir & Baleanu, Dumitru, 2020. "Stationary distribution and extinction of stochastic coronavirus (COVID-19) epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    8. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    9. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
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    Cited by:

    1. Ruichao Li & Xiurong Guo, 2024. "Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence," Mathematics, MDPI, vol. 12(3), pages 1-17, January.

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