IDEAS home Printed from https://ideas.repec.org/a/gam/jjopen/v4y2021i2p8-100d547347.html
   My bibliography  Save this article

Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

Author

Listed:
  • Nita H. Shah

    (Department of Mathematics, Gujarat University, Ahmedabad 380009, India)

  • Ankush H. Suthar

    (Department of Mathematics, Gujarat University, Ahmedabad 380009, India)

  • Ekta N. Jayswal

    (Department of Mathematics, Gujarat University, Ahmedabad 380009, India)

  • Ankit Sikarwar

    (Department of Development Studies, International Institute for Population Sciences, Mumbai 400088, India)

Abstract

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model’s transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

Suggested Citation

  • Nita H. Shah & Ankush H. Suthar & Ekta N. Jayswal & Ankit Sikarwar, 2021. "Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India," J, MDPI, vol. 4(2), pages 1-15, April.
    • Handle: RePEc:gam:jjopen:v:4:y:2021:i:2:p:8-100:d:547347
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-8800/4/2/8/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-8800/4/2/8/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rafiq, Danish & Suhail, Suhail Ahmad & Bazaz, Mohammad Abid, 2020. "Evaluation and prediction of COVID-19 in India: A case study of worst hit states," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Mahajan, Ashutosh & Sivadas, Namitha A & Solanki, Ravi, 2020. "An epidemic model SIPHERD and its application for prediction of the spread of COVID-19 infection in India," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. N. Shamsi Gamchi & M. Esmaeili, 2023. "A novel mathematical model for prioritization of individuals to receive vaccine considering governmental health protocols," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 24(4), pages 633-646, June.

    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. Xiaojin Xie & Kangyang Luo & Zhixiang Yin & Guoqiang Wang, 2021. "Nonlinear Combinational Dynamic Transmission Rate Model and Its Application in Global COVID-19 Epidemic Prediction and Analysis," Mathematics, MDPI, vol. 9(18), pages 1-17, September.
    2. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    3. Katarzyna Czech & Anna Davy & Michał Wielechowski, 2021. "Does the COVID-19 Pandemic Change Human Mobility Equally Worldwide? Cross-Country Cluster Analysis," Economies, MDPI, vol. 9(4), pages 1-19, November.
    4. Lokman Gunduz & Ahmet Faruk Aysan & Rifgi Bugra Bagci & Hatice Karahan, 2024. "Explosive Behavior in COVID-19 and Policy Responses: Lessons Learned for Public Health Management," SAGE Open, , vol. 14(1), pages 21582440231, March.
    5. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(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:jjopen:v:4:y:2021:i:2:p:8-100:d:547347. 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.