Mathematical Modeling and Analysis of HIV Transmission in Bandung City, Indonesia

HIV remains a major public health concern in urban areas of Indonesia, including Bandung City. Understanding its transmission dynamics is essential for designing effective control strategies. This study develops a mathematical model of HIV transmission incorporating real epidemiological data from Bandung City. The population is divided into several compartments representing susceptible individuals, HIV-infected individuals, and individuals under treatment. A nonlinear treatment function is introduced to reflect limited medical resources and treatment saturation effects. Model parameters are estimated using reported HIV case data through a data fitting procedure based on a Genetic Algorithm (GA), which minimizes the difference between model simulations and observed data. This approach allows efficient exploration of the parameter space and provides reliable parameter estimates for the transmission and treatment processes. Based on the estimated parameters, the basic reproduction number is derived analytically and its estimated value is 2.56, indicating that the infection can persist in the population. Stability analysis of the disease-free and endemic equilibrium points is performed using linearization techniques. Furthermore, bifurcation analysis is conducted to investigate qualitative changes in system behavior with respect to key parameters, particularly the transmission rate and treatment effectiveness. Numerical simulations are presented to validate the analytical results and to illustrate the impact of nonlinear treatment and parameter variations on HIV transmission dynamics. The results show that nonlinear treatment significantly influences the stability of equilibria and may lead to backward bifurcation under certain conditions. This study provides a realistic mathematical framework for analyzing HIV transmission in Bandung City and offers valuable insights for optimizing HIV control and treatment policies.