Pemodelan Matematika dan Analisis Kestabilan Model Pada Penyebaran HIV/AIDS Tipe SITA (Susceptible, Infected, Treatment, AIDS) - Mahuda, Isnaini; Rofiroh, Rofiroh (UIN Imam Bonjol Padang, 2024)
HIV/AIDS still become a major public health problem that occurs in almost all countries in the world. Until now, no medicine has been found that can treat HIV/AIDS. However, there is therapy or treatment that can be done to slow the spread of the virus, namely antiretroviral (ARV) or called Antiretroviral Therapy (ART). The mathematical modeling carried out in this study uses the SITA type where there are 4 compartments, namely Susceptible (S), Infected (I) Treatment (T), and AIDS (A) in a closed population. The objectives of this research are: 1) to construct a mathematical model for the spread of SITA type HIV/AIDS, 2) determine the equilibrium point and stability of the equilibrium point of the model, 3) determine the basic reproduction number (R_0), and 4) carry out a dynamic simulation of the model. Mathematical modeling of the spread of SITA type HIV/AIDS produces two equilibrium points, namely the disease-free equilibrium point (E_1) and the endemik equilibrium point (E_2). From the results of the analysis, the basic reproduction ratio (R_0) was also obtained by building a matrix called the Next Generation Matrix (NGM). The basic reproduction ratio number (R_0) also determines the existence and stability of the equilibrium point and can control the rate of spread of HIV/AIDS. Based on the simulation results, the parameter value that greatly influences population dynamics is the rate of treatment given to the Infected (I) sub population.