Stability Analysis and Estimation of the Basic Reproductive Ratio Using a SEITA-Type Model of HIV/AIDS Spread in Cilegon City

HIV/AIDS remains a critical global health issue that requires a multidisciplinary approach to reduce its transmission. Understanding the transmission dynamics through mathematical models can assist in formulating effective intervention strategies. This study aims to analyze the stability of HIV/AIDS transmission model in Cilegon City using five compartments, namely Susceptible, Educated, Infected, Treatment, and AIDS or SEITA-type model. Subsequently, the basic reproductive ratio (R0) is estimated by constructing the Next Generation Matrix (NGM) and the dynamic simulation of the model is carried out using parameters calibrated based on HIV/AIDS data from Cilegon City. The Analysis of stability equilibrium points show that the disease-free equilibrium point is locally asymptotically stable when R0<1 and when R0>1 then endemic equilibrium point is locally asymptotically stable. Furthermore, the numeric simulation results indicate that the increasing parameter transition rate from the susceptible subpopulation to the educated subpopulation, the ARV treatment rate applied to the infected subpopulation and decreasing parameter transition rate from the educated subpopulation to the susceptible subpopulation, could suppress the basic reproduction number, thereby enabling effective control of the HIV/AIDS spread in Cilegon City.