ANALISIS MODEL MATEMATIKA ORDE FRAKSIONAL PENYEBARAN PENYAKIT HIV/AIDS DENGAN PENGOBATAN - Mustakim (PT Innovative Academic Journals, 2025)
AIDS is a collection of symptoms of infectious diseases that arise as a result of the weakened immune system of the patient, caused by the HIV (Human Immunodeficiency Virus). Mathematical models play an important role in understanding the dynamics of HIV/AIDS transmission, especially with the presence of treatment, and can be used to predict its spread through numerical simulations of the mathematical model of HIV/AIDS transmission with treatment. This research discusses the analysis of a fractional-order mathematical model of HIV/AIDS transmission with treatment. The model is a modification of the nonlinear Ordinary Differential Equation (ODE) system into a Fractional Differential Equation (FDE) system. Generally, solutions to nonlinear ODEs are difficult to find analytically. However, a mathematical model that can be solved analytically is the Fractional Differential Equation (FDE) system. One method for solving FDEs is using the Homotopy Perturbation Method (HPM), which transforms the FDE into a Homotopy Differential Equation system by multiplying each equation in the FDE with an embedding parameter (p). The solution is expressed as an infinite series, which is then solved numerically. As the fractional derivative order increases, the changes in the graph of the healthy population susceptible to HIV/AIDS infection, the population infected with HIV/AIDS, the population with full-blown AIDS not receiving ARV treatment, the population receiving ARV treatment, and the healthy population changing lifestyle patterns, become faster.