HIV/AIDS Dynamics Epidemic Analysis Through Age Group and Internal Competition Influence

Abstract

Transmission of HIV/AIDS in Indonesia has potential rounding into very hard. How situation of HIV/AIDS epidemics in Indonesia in future still is unclear. This research aims to analyze of HIV/AIDS epidemics dynamics with influence of age group and internal competition through the simple mathematics model. The SI compartment model is obtained by translating mechanism spreading of disease to be presented in the form of system of nonlinear differential equations. The model parameters obtained by estimation use data of HIV/AIDS in Indonesia from relevant literatures. The local and global stability for the equilibrium point is described use analysis of eigenvalues of Jacobian matrix and Lyapunov-LaSalle’s invariant principle. For the case of data of HIV/AIDS in Indonesia 2007, threshold values of infected reproduced ratio, R₀= 0.000035 susceptible reproduced ratio, R₁= 100.60235 and infection contact rate, R₂=3.50192 The HIV/AIDS dynamics model with two age groups and internal competition has a unique disease-free equilibrium point. The disease-free equilibrium point E₀*= (34258263.6455834, 0, 0) is locally asymptotically stable and global unstable.