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This study aims to quantitatively analyze a mathematical model of HIV/AIDS transmission that includes both vertical transmission and nonlinear treatment effects. Unlike traditional integer-order derivatives, fractional derivatives better capture the memory effects inherent in biological systems. Therefore, the classical HIV/AIDS transmission model is extended to a fractional-order model using the Atangana–Baleanu–Caputo (ABC) derivative. The existence and uniqueness of solutions are established using the fixed-point theorem. Furthermore, numerical simulations are conducted using the Toufik–Atangana method, which incorporates the ABC derivative. The effects of various biological parameters on the dynamics of disease transmission are explored, and the results are presented graphically.

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Analysis of Fractional Order HIV/AIDS Model Incorporating Vertical Transmission and Non-linear Treatment via Toufik–Atangana Scheme

  • 会议论文

  • 发表日期：

    2026年

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  • Shubhashree Sahu,
  • Praveen Kumar Gupta,
  • Arpita Devi

摘要

This study aims to quantitatively analyze a mathematical model of HIV/AIDS transmission that includes both vertical transmission and nonlinear treatment effects. Unlike traditional integer-order derivatives, fractional derivatives better capture the memory effects inherent in biological systems. Therefore, the classical HIV/AIDS transmission model is extended to a fractional-order model using the Atangana–Baleanu–Caputo (ABC) derivative. The existence and uniqueness of solutions are established using the fixed-point theorem. Furthermore, numerical simulations are conducted using the Toufik–Atangana method, which incorporates the ABC derivative. The effects of various biological parameters on the dynamics of disease transmission are explored, and the results are presented graphically.