Global Stability Analysis of HIV+ Model

We developed and studied a mathematical model of HIV+. Two equilibriums points were found, disease free and endemic equilibrium, and basic reproduction ratio \( R_{0} \) was also calculated by the use of next generation matrix. Global stability analysis of the equilibria was carried out by the use of Lyapunov function, and it was shown that the stability of the equilibria depends on the magnitude of the basic reproduction ratio. When \( R_{0} < 1 \), the disease free equilibrium is globally asymptotically stable, and disease dies out. On the other hand if \( R_{0} \ge 1 \), the endemic equilibrium is globally asymptotically stable and epidemics occurs. Reported cases of 13646 HIV-1 positive were obtained in the year 2016 from Ministry of Health, Turkey (MOH). This data is used to present the numerical simulations, which supports the analytic result. \( R_{0} \) was found to be 1.98998, which is bigger than 1, this shows the threat posed by HIV in Turkey.