Batik Motif of a Mathematical Model for The Spread of HIV/Aids with Education and Art Treatment

Abstract

Mathematical modeling plays a crucial role in understanding the dynamics of infectious disease transmission, including HIV/AIDS. This study examines a mathematical model of HIV/AIDS spread that incorporates public awareness education and Antiretroviral Therapy (ART) treatment. The proposed model is a modification of the SITA model by adding a compartment of susceptible individuals who are aware of HIV/AIDS transmission risks, along with parameters representing education rate and treatment effectiveness. The analysis focuses on the existence and stability of equilibrium points as well as the basic reproduction number (). The results reveal two equilibrium points: the disease-free and endemic equilibria. The disease-free equilibrium is locally asymptotically stable when , indicating the eventual eradication of the disease, whereas  1 leads to an endemic state. Numerical simulations confirm that increased education and effective ART treatment significantly reduce the number of infected individuals. These findings highlight the critical role of educational interventions and ART programs in controlling the spread of HIV/AIDS.