Construction of novel plethora of soliton solutions for conformable fractional HIV-1 infection model

In this research study, an analytical examination of a conformable fractional mathematical equation that models CD4+ T-cell infection by HIV-1 is provided. To examine the multifaceted nature of HIV-1 infection and discover valuable information about the mechanism of its spread in the group of CD4+ T-cells, we construct soliton solutions of the proposed model using Extended Direct Algebraic Method (EDAM). The suggested EDAM converts the targeted model into a nonlinear algebraic system by proposing closed form travelling solutions. Analytically solving the resultant algebraic system with a symbolic computation tool Maple yields a new range of solutions in the form of rational, trigonometric, hyperbolic and exponential functions. The study also provides an array of 2D graphic representations that depict the accuracy of the findings made out of the analytical process. The resulting wave profiles, which show the strong dynamics of the model, include kink waves, periodic waves, lump waves, amplified waves, and damp waves. The derived soliton solutions help to explain the system’s behavior and improve the correctness of the mathematical model proposed to describe the intricate dynamics that take place between the virus and CD4+ T-cells throughout infection. The finding of this research work gives a helpful support for future study on the effects of antiviral medicine therapy on HIV-1 infection.