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Mathematical Modelling of HIV/AIDS Treatment Using Caputo–Fabrizio Fractional Differential Systems

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Abstract

The focus of this study lies in developing and evaluating a Caputo–Fabrizio fractional derivative model that encapsulates the dynamics of the worldwide HIV/AIDS epidemic while integrating an antiretroviral therapy component. The methodology involves employing iterative techniques alongside the fixed-point theorem to establish the existence and uniqueness solutions of the model. In particular, the model identifies equilibrium points corresponding to disease outbreaks and disease-free scenarios. Additionally, it showcases the local asymptotic stability of the disease-free equilibrium point and outlines the criteria for the presence of the endemic equilibrium point. The findings verify that as the fractional order decreases, the disease-free equilibrium point becomes more stable. To demonstrate the impact of altering the fractional order and to bolster the theoretical finding, numerical simulations are conducted over the fractional order range.

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Acknowledgements

The authors Kamal Shah and Thabet Abdeljawad would like to thank Prince Sultan University for the support through the TAS research lab.

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Authors and Affiliations

  1. Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R &D Institute of Science and Technology, Chennai, India

    S. Manikandan, T. Gunasekar & K. A. Venkatesan

  2. School of Artificial Intelligence and Data Science, Indian Institute of Technology (IIT), Jodhpur, Rajasthan, India

    T. Gunasekar

  3. Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Sidi Othman, Casablanca, Morocco

    A. Kouidere

  4. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia

    Kamal Shah & Thabet Abdeljawad

  5. Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber, Pakhtunkhwa, 18000, Pakistan

    Kamal Shah

  6. Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

    Thabet Abdeljawad

  7. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Republic of Korea

    Thabet Abdeljawad

  8. Department of Mathematics and Applied Mathematics School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

    Thabet Abdeljawad

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  1. S. Manikandan
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  2. T. Gunasekar
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  4. K. A. Venkatesan
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  5. Kamal Shah
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The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

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Manikandan, S., Gunasekar, T., Kouidere, A. et al. Mathematical Modelling of HIV/AIDS Treatment Using Caputo–Fabrizio Fractional Differential Systems. Qual. Theory Dyn. Syst. 23, 149 (2024). https://doi.org/10.1007/s12346-024-01005-z

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