IDEAS home Printed from https://ideas.repec.org/a/gam/jijerp/v20y2023i2p939-d1025169.html
   My bibliography  Save this article

Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric Analysis

Author

Listed:
  • Mohammad AlShurbaji

    (Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

  • Lamis Abdul Kader

    (Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

  • Hadia Hannan

    (Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

  • Maruf Mortula

    (Department of Civil Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

  • Ghaleb A. Husseini

    (Department of Chemical and Biological Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
    Material Science and Engineering PhD Program, College of Arts and Sciences, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates)

Abstract

Diabetes is sweeping the world as a silent epidemic, posing a growing threat to public health. Modeling diabetes is an effective method to monitor the increasing prevalence of diabetes and develop cost-effective strategies that control the incidence of diabetes and its complications. This paper focuses on a mathematical model known as the diabetes complication (DC) model. The DC model is analyzed using different numerical methods to monitor the diabetic population over time. This is by analyzing the model using five different numerical methods. Furthermore, the effect of the time step size and the various parameters affecting the diabetic situation is examined. The DC model is dependent on some parameters whose values play a vital role in the convergence of the model. Thus, parametric analysis was implemented and later discussed in this paper. Essentially, the Runge–Kutta (RK) method provides the highest accuracy. Moreover, Adam–Moulton’s method also provides good results. Ultimately, a comprehensive understanding of the development of diabetes complications after diagnosis is provided in this paper. The results can be used to understand how to improve the overall public health of a country, as governments ought to develop effective strategic initiatives for the screening and treatment of diabetes.

Suggested Citation

  • Mohammad AlShurbaji & Lamis Abdul Kader & Hadia Hannan & Maruf Mortula & Ghaleb A. Husseini, 2023. "Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric Analysis," IJERPH, MDPI, vol. 20(2), pages 1-23, January.
    • Handle: RePEc:gam:jijerp:v:20:y:2023:i:2:p:939-:d:1025169
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1660-4601/20/2/939/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1660-4601/20/2/939/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Abdelfatah Kouidere & Abderrahim Labzai & Hanane Ferjouchia & Omar Balatif & Mostafa Rachik, 2020. "A New Mathematical Modeling with Optimal Control Strategy for the Dynamics of Population of Diabetics and Its Complications with Effect of Behavioral Factors," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-12, June.
    2. Hannah Al Ali & Alireza Daneshkhah & Abdesslam Boutayeb & Zindoga Mukandavire, 2022. "Examining Type 1 Diabetes Mathematical Models Using Experimental Data," IJERPH, MDPI, vol. 19(2), pages 1-20, January.
    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. Farman, Muhammad & Ahmad, Aqeel & Zehra, Anum & Nisar, Kottakkaran Sooppy & Hincal, Evren & Akgul, Ali, 2024. "Analysis and controllability of diabetes model for experimental data by using fractional operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 133-148.

    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. Farman, Muhammad & Ahmad, Aqeel & Zehra, Anum & Nisar, Kottakkaran Sooppy & Hincal, Evren & Akgul, Ali, 2024. "Analysis and controllability of diabetes model for experimental data by using fractional operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 133-148.
    2. Kouidere, Abdelfatah & Balatif, Omar & Rachik, Mostafa, 2021. "Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Kouidere, Abdelfatah & Youssoufi, Lahcen EL & Ferjouchia, Hanane & Balatif, Omar & Rachik, Mostafa, 2021. "Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with Cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    4. Nasir, Hanis, 2022. "On the dynamics of a diabetic population model with two delays and a general recovery rate of complications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 571-602.
    5. Karim El Moutaouakil & Abdellatif El Ouissari & Vasile Palade & Anas Charroud & Adrian Olaru & Hicham Baïzri & Saliha Chellak & Mouna Cheggour, 2023. "Multi-Objective Optimization for Controlling the Dynamics of the Diabetic Population," Mathematics, MDPI, vol. 11(13), pages 1-28, July.

    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:jijerp:v:20:y:2023:i:2:p:939-:d:1025169. 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.