Model Matematika Penyebaran HIV/AIDS dengan Edukasi Kesehatan

Abstract

In this research has been carried out the stability analysis of HIV/AIDS epidemic model with a public health educational through the expansion of the SI (susceptible-infected) model. In modeling of HIV/AIDS epidemic, the population is divided into six subpopulations: uneducated susceptible individuals, educated susceptible individuals, uneducated infected individuals without AIDS symptoms, educated infected individuals with AIDS symptoms, uneducated infected individuals with AIDS symptoms and educated infected individuals with AIDS symptoms. The disease-free equilibrium point of the HIV transmission model with education program is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. The endemic equilibrium point is exist if the effective reproduction number is greater than unity and stability of endemic equilibrium point has been determined using the Center manifold theory. The center manifold theory can be used to analyze the stability near the disease-free equilibrium point (the effective reproduction number is equal to unity). The impact of a public health education on the spread of HIV/AIDS, the sensitivity analysis on effective reproduction numbers respect to all the parameters which drive the disease dynamics.