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Existence and Sensitivity Analysis of a Caputo Fractional-Order Diphtheria Epidemic Model

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  • Idris Ahmed

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa, Kafin Hausa P.M.B 048, Jigawa State, Nigeria
    These authors contributed equally to this work.)

  • Chanakarn Kiataramkul

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Mubarak Muhammad

    (Department of Physiology, Neuroscience Program, Faculty of Medicine, Khon Kaen University, Khon Kaen 40002, Thailand
    These authors contributed equally to this work.)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

Abstract

Diphtheria, a potentially life-threatening infectious disease, is primarily caused by the bacterium Corynebacterium diphtheriae . This pathogen induces a range of severe symptoms, including respiratory distress, cardiac arrhythmias, and, in extreme cases, fatal outcomes. This paper aim to unravel the transmission dynamics of diphtheria infection within the Caputo fractional derivatives framework, establishing the solutions’ existence and uniqueness. Through forward normalized sensitivity analysis, we scrutinize the key parameters influencing the basic reproduction number, a pivotal metric in understanding and controlling the spread of the disease. The results indicate that reducing the values of the interaction rate, transmission rate, and birth rate plays a key role in curtailing diphtheria transmission. Furthermore, employing an effective numerical tool, we present graphical representations that delineate the influence of various crucial model parameters on infection dynamics.

Suggested Citation

  • Idris Ahmed & Chanakarn Kiataramkul & Mubarak Muhammad & Jessada Tariboon, 2024. "Existence and Sensitivity Analysis of a Caputo Fractional-Order Diphtheria Epidemic Model," Mathematics, MDPI, vol. 12(13), pages 1-18, June.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2033-:d:1425928
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    References listed on IDEAS

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    1. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Doungmo Goufo, Emile F. & Khan, Yasir & Chaudhry, Qasim Ali, 2020. "HIV and shifting epicenters for COVID-19, an alert for some countries," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Wahab A. Iddrisu & Inusah Iddrisu & Abdul-Karim Iddrisu & Keshlan S. Govinder, 2023. "Modeling Cholera Epidemiology Using Stochastic Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2023, pages 1-17, May.
    4. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. A. Mhlanga & Xiaohua Ding, 2021. "Dynamics of HSV-2 in the Presence of Optimal Counseling and Education among Prisoners," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-18, June.
    6. Sung Kyu Choi & Bowon Kang & Namjip Koo, 2014. "Stability for Caputo Fractional Differential Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    Full references (including those not matched with items on IDEAS)

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