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

Idris Ahmed, Chanakarn Kiataramkul, Mubarak Muhammad and Jessada Tariboon ()
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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
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
Mubarak Muhammad: Department of Physiology, Neuroscience Program, Faculty of Medicine, Khon Kaen University, Khon Kaen 40002, Thailand
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

Mathematics, 2024, vol. 12, issue 13, 1-18

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.

Keywords: diphtheria; mathematical model; existence results; sensitivity analysis; numerical results (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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