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Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India

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  • Verma, Lalchand
  • Meher, Ramakanta
  • Pandya, Darshak P.

Abstract

This work considers a temporal fractional HIV/AIDS model with fractal dimensions to examine the influence of awareness on the dynamics of HIV/AIDS. It investigates an epidemiological model of the dynamics of HIV/AIDS transmission in India using actual data from 1990 to 2016 to authenticate the proposed model. The Picard–Lindelof approach is employed to demonstrate the uniqueness and existence of the solutions where the stability analysis is done with the disease-free equilibrium point and basic reproduction number R0. The Adams–Bashforth method employs a two-step Lagrange polynomial in the generalised power-law kernel form to obtain the proposed model’s numerical solution. Finally, the least square curve fitting method is used to estimate the parametric study of the proposed model with the actual data on HIV cases reported in India from 1990 to 2016.

Suggested Citation

  • Verma, Lalchand & Meher, Ramakanta & Pandya, Darshak P., 2025. "Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 135-150.
    • Handle: RePEc:eee:matcom:v:234:y:2025:i:c:p:135-150
    DOI: 10.1016/j.matcom.2025.02.011
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    References listed on IDEAS

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    1. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Zhai, Xuanpei & Li, Wenshuang & Wei, Fengying & Mao, Xuerong, 2023. "Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    4. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    5. Silva, Cristiana J. & Torres, Delfim F.M., 2019. "Stability of a fractional HIV/AIDS model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 164(C), pages 180-190.
    6. Fatmawati, & Khan, Muhammad Altaf & Odinsyah, Hafidz Putra, 2020. "Fractional model of HIV transmission with awareness effect," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Saif Ullah & Mohamed Altanji & Muhammad Altaf Khan & Ahmed Alshaheri & Wojciech Sumelka, 2023. "The Dynamics Of Hiv/Aids Model With Fractal-Fractional Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-20.
    8. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2021. "A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1003-1026.
    9. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    10. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
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