IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i11p1678-d1403733.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/11/1678/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/11/1678/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sharma, Natasha & Verma, Atul Kumar & Gupta, Arvind Kumar, 2021. "Spatial network based model forecasting transmission and control of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    2. Vincenzo Alfano & Salvatore Ercolano, 2020. "The Efficacy of Lockdown Against COVID-19: A Cross-Country Panel Analysis," Applied Health Economics and Health Policy, Springer, vol. 18(4), pages 509-517, August.
    3. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Vincenzo Alfano & Salvatore Ercolano, 2022. "Stay at Home! Governance Quality and Effectiveness of Lockdown," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 159(1), pages 101-123, January.
    5. Vincenzo Alfano, 2022. "The Effects of School Closures on COVID-19: A Cross-Country Panel Analysis," Applied Health Economics and Health Policy, Springer, vol. 20(2), pages 223-233, March.
    6. Nadim, Sk Shahid & Chattopadhyay, Joydev, 2020. "Occurrence of backward bifurcation and prediction of disease transmission with imperfect lockdown: A case study on COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Imdad, Kashif & Sahana, Mehebub & Rana, Md Juel & Haque, Ismail & Patel, Priyank Pravin & Pramanik, Malay, 2020. "The COVID-19 pandemic's footprint in India: An assessment on the district-level susceptibility and vulnerability," MPRA Paper 100727, University Library of Munich, Germany.
    8. Gaetano Perone, 2022. "Comparison of ARIMA, ETS, NNAR, TBATS and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 23(6), pages 917-940, August.
    9. Sebastien Bourdin & Slimane Ben Miled & Jamil Salhi, 2022. "The Drivers of Policies to Limit the Spread of COVID-19 in Europe," JRFM, MDPI, vol. 15(2), pages 1-9, February.
    10. Alfano, Vincenzo & Ercolano, Salvatore, 2022. "Back to school or … back to lockdown? The effects of opening schools on the diffusion of COVID-19 in Italian regions," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    11. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    12. Rubayyi T. Alqahtani & Abdelhamid Ajbar, 2021. "Study of Dynamics of a COVID-19 Model for Saudi Arabia with Vaccination Rate, Saturated Treatment Function and Saturated Incidence Rate," Mathematics, MDPI, vol. 9(23), pages 1-13, December.
    13. Moran Bodas & Bruria Adini & Eli Jaffe & Arielle Kaim & Kobi Peleg, 2022. "Lockdown Efficacy in Controlling the Spread of COVID-19 May Be Waning Due to Decline in Public Compliance, Especially among Unvaccinated Individuals: A Cross-Sectional Study in Israel," IJERPH, MDPI, vol. 19(9), pages 1-11, April.
    14. Vincenzo Alfano & Salvatore Ercolano & Lorenzo Cicatiello, 2020. "A Synthetic Control Method Analysis of Schools Opening and Covid-19 Outbreak in Italy," CESifo Working Paper Series 8784, CESifo.
    15. Alfano, Vincenzo & Ercolano, Salvatore & Cicatiello, Lorenzo, 2021. "School openings and the COVID-19 outbreak in Italy. A provincial-level analysis using the synthetic control method," Health Policy, Elsevier, vol. 125(9), pages 1200-1207.
    16. Wang, Xueli & Zhang, Suxia, 2024. "Coupling media coverage and susceptibility for modeling epidemic dynamics: An application to COVID-19," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 374-394.
    17. Rahil Changotra & Himadri Rajput & Prachi Rajput & Sneha Gautam & Amarpreet Singh Arora, 2021. "Largest democracy in the world crippled by COVID-19: current perspective and experience from India," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(5), pages 6623-6641, May.
    18. Shyamali Satpathy & Gokulananda Patel & Khushboo Kumar, 2021. "Identifying and ranking techno-stressors among IT employees due to work from home arrangement during Covid-19 pandemic," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 48(4), pages 391-402, December.
    19. Tarifa S. Almulhim & Igor Barahona, 2022. "Decision support system for ranking relevant indicators for reopening strategies following COVID-19 lockdowns," Quality & Quantity: International Journal of Methodology, Springer, vol. 56(2), pages 463-491, April.
    20. Nadim, Sk Shahid & Ghosh, Indrajit & Chattopadhyay, Joydev, 2021. "Short-term predictions and prevention strategies for COVID-19: A model-based study," Applied Mathematics and Computation, Elsevier, vol. 404(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1678-:d:1403733. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.