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Dynamics of a Model of Coronavirus Disease with Fear Effect, Treatment Function, and Variable Recovery Rate

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  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Abdelhamid Ajbar

    (Department of Chemical Engineering, King Saud University, Riyadh 11362, Saudi Arabia)

  • Nadiyah Hussain Alharthi

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

Abstract

In this work, we developed, validated, and analysed the behaviour of a compartmental model of COVID-19 transmission in Saudi Arabia. The population was structured into four classes: susceptible (S), exposed (E), infectious (I), and removed (R) individuals. This SEIR model assumes a bilinear incidence rate and a nonlinear recovery rate that depends on the quality of health services. The model also considers a treatment function and incorporates the effect of fear due to the disease. We derived the expression of the basic reproduction number and the equilibrium points of the model and demonstrated that when the reproduction number is less than one, the disease-free equilibrium is stable, and the model predicts a backward bifurcation. We further found that when the reproduction number is larger than one, the model predicts stable periodic behaviour. Finally, we used numerical simulations with parameter values fitted to Saudi Arabia to analyse the effects of the model parameters on the model-predicted dynamic behaviours.

Suggested Citation

  • Rubayyi T. Alqahtani & Abdelhamid Ajbar & Nadiyah Hussain Alharthi, 2024. "Dynamics of a Model of Coronavirus Disease with Fear Effect, Treatment Function, and Variable Recovery Rate," Mathematics, MDPI, vol. 12(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1678-:d:1403733
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    References listed on IDEAS

    as
    1. Chandan Maji, 2021. "Impact of Media-Induced Fear on the Control of COVID-19 Outbreak: A Mathematical Study," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-11, February.
    2. Sardar, Tridip & Nadim, Sk Shahid & Rana, Sourav & Chattopadhyay, Joydev, 2020. "Assessment of lockdown effect in some states and overall India: A predictive mathematical study on COVID-19 outbreak," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Soheyl Khalilpourazari & Hossein Hashemi Doulabi, 2023. "Robust modelling and prediction of the COVID-19 pandemic in Canada," International Journal of Production Research, Taylor & Francis Journals, vol. 61(24), pages 8367-8383, December.
    4. Buonomo, Bruno & Giacobbe, Andrea, 2023. "Oscillations in SIR behavioural epidemic models: The interplay between behaviour and overexposure to infection," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    Full references (including those not matched with items on IDEAS)

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