EXPANSION METHOD FOR SOLVING FRACTIONAL ORDER HIV/AIDS MODEL (FUDMA JOURNAL OF SCIENCES, 2025)
This work focused on application of non-integer order derivative to solve a system of differential equations governing a nonlinear HIV/AIDS model. The model was formulated based on the efficacy of the administered anti-retrovirus therapy (ART) in abating the destructive effect of the exponential growth of the causative virus, together with time effect analysis of the impact of the drug on both healthy and infected cells within the host. Two of the most important antibodies were considered in the development of the model, the Clusters of differentiation 4 (CD4) cells and Macrophages. Their impact on the overall metabolic system of healthy and HIV infected human are modeled mathematically as a system of nonlinear differential equation. Some basic definitions of known fractional operators were adopted and applied to the model equation. The Caputo fractional derivative equivalent of the model equations was methodically solved using the expansion method of solution, numerically simulated using the Maple 18 in-built standard Runge-Kutta order 4 method, and the graph was plotted for various values of from 0.5 1. The result revealed the pattern of each compartments within the time frame, and it can be deduced from the graph that early discovery of the infection together with therapy can significantly lower the exponential growth rate of the virus, which in turn will culminate in healthy lifestyle for the carrier.
Keywords: ART; Macrophages; Caputo; Fractional derivative; Simulate; Runge-Kutta