Abstract
HIV/AIDS is a disease caused by a virus that attacks the immune system, causing the body's immunity to decrease. In this study, the SI (Susceptible-Infected) mathematical model will be studied to analyze the stability of the HIV/AIDS epidemic model, especially in the Special Province of Yogyakarta (DIY) based on age group and population density. The age group is divided into two subpopulations, namely children and adults. The analysis carried out is to determine the local and global stability of the equilibrium point of the disease-free and disease-infected model. The analysis uses the characteristic equation of the Jacobi matrix and the Lyapunov-La Salle invariance principle or uses the conditions of the threshold value of susceptible reproduction ratio (R1), infected reproduction ratio (R0), and infectious contact rate. (R2). For cases of HIV/AIDS data in the Province of the Special Region of Yogyakarta (DIY) with an initial population of 2016, obtained R0 = 0.027, R1 = 114.25, R2 = 0.93. For cases of HIV/AIDS data in the Province of the Special Region of Yogyakarta (DIY) with an initial population of 2016, obtained E1 = (924.280, 179.402, 0, 0). The disease-free equilibrium point is globally asymptotically stable, meaning that if the parameter values do not change then there are no infected individuals and the susceptible subpopulation of children and adults to a constant positive value.
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