Qualitative and quantitative analysis of a fractal fractional HIV/AIDS model

Abstract

The fractal-fractional derivative is a type of fractional derivative that is more broadly applicable. This method is used to investigate a variety of real-world issues. This work focuses on investigating a fractional derivative-based sustainable strategy for the dynamics of HIV/AIDS. For the representation of a time-fractional order HIV/AIDS model, we presented a system of FDEs. The suggested model’s uniqueness and existence are revealed through equilibrium analysis. Analysis of the fractional order is accomplished using both sensitivity analysis and qualitative analysis. The first and second derivative tests are used to validate the analysis of the Lyapunov function for global stability. Solutions are produced using a two-step Lagrange polynomial in the generalized form of the Mlittag-Lefler kernel to analyze the influence of the fractional operator, which illustrates the impact of HIV/AIDS on society. Such an inquiry will help in the comprehension of HIV/AIDS behavior and the creation of preventative measures for the infected. Graphical representations of sensitive criteria that illustrate how to reduce and eradicate HIV/AIDS in society are provided. Finally, it is demonstrated that the smaller values of fractal-fractional order perform better than bigger values for all compartments of the proposed model of HIV/AIDS. We continue to believe that our work will be helpful to researchers working in diverse fields of applied science and engineering.

Keywords

• HIV/AIDS
• Epidemic model
• Lyapunov function
• Fixed point theorem
• FFM operator
• Numerical simulation