Journal of Advances in Mathematics and Computer Science

This study presents a mathematical model for the weekly prediction of Human Immunodeficiency Virus (HIV) infection dynamics in CD4⁺ T-cells incorporating a cure factor and a nonlinear fractional-order regulatory effect. The model captures the interactions among uninfected target CD4⁺ T-cells, infected cells, and free virus particles, where the nonlinear exponent  represents regulatory and memory effects in the immune response. The basic reproduction number R₀ is derived using the next-generation matrix approach and is shown to play a critical role in determining the stability of the disease-free and endemic equilibria. Stability analysis reveals that the disease-free equilibrium is locally asymptotically stable when R₀>1, while the endemic equilibrium emerges and persists when R₀>1. Numerical simulations are carried out to investigate the effects of varying the fractional-order parameter k and the cure factor p on the system dynamics. The simulations demonstrate that increasing the cure factor significantly reduces the infected cell population and viral load, leading to faster disease clearance. Bifurcation analysis with respect to k  reveals a critical threshold beyond which viral persistence occurs, highlighting the sensitivity of HIV dynamics to nonlinear regulatory mechanisms. The results further show that lower values of k and higher values of ρ effectively reduce the reproduction number below unity, suppressing viral replication. Therefore, the model provides important insights into the combined influence of nonlinear immune regulation and therapeutic cure mechanisms on HIV infection dynamics. The findings underscore the importance of controlling the reproduction number through both biological regulation and treatment strategies, offering a valuable framework for understanding HIV progression and potential intervention policies.