OPTIMAL CONTROL ANALYSIS OF HIV/AIDS DISEASE SPREAD MODEL IN INDONESIA

Abstract

The Human Immunodeficiency Virus (HIV) is a contagious virus that weakens the immune system of infected individuals, making them more susceptible to various diseases. These individuals are referred to as those exposed to the AIDS disease, which unfortunately, cannot be cured. To effectively manage AIDS, prevention is crucial in slowing down the spread and growth of the HIV virus. Mathematical modeling can play a significant role in the optimal control of AIDS. In this study, the , , , , model with three different optimal controls were employed. Optimal control involves public health education campaigns, screening, and treatment. The goal is to minimize the number of individuals infected with HIV/AIDS using Pontryagin's Maximum Principle. This principle considers various factors, such as population class coefficients, cost weights, and control variables to determine the most effective approach. The simulation results indicate that counseling control in the exposed population class ( ) yields better outcomes compared to counseling control in the susceptible class and treatment control in the HIV-infected population class. This implies that focusing on educating and counseling individuals who are exposed to HIV can be more efficient in AIDS control than targeting those already infected or at risk. By applying these optimal control strategies, it may be possible to mitigate the impact of HIV/AIDS and improve public health outcomes.