摘要：We propose mathematical model of HIV/AIDSwith two different stages of infection subpopulation. The proposed model is more realistic since it establishes the compartment diagram based on data from the Indonesian Ministry ofHealth. The model consists of six compartments (susceptible,infected with and without treatment, AIDS, treatment, andrecovered sub populations). We analyzed the model by provingthe positivity and boundedness of the models solutions. Furthermore, we analyzed local and global stability of the solutionsdetermined by the basic reproduction number as a threshold ofdisease transmission. The disease-free and endemic equilibriumpoints are locally asymptotically stable when R0 < 1 andR0 > 1 respectively. For global stability, we constructedthe Lyapunov function. The results indicate that the diseasefree equilibrium point is globally asymptotically stable whenR0 < 1 and that the endemic equilibrium point is globallyasymptotically stable when R0 > 1. We conducted numericalsimulation to support the analytical results.
关键词：dynamical system; HIV/AIDS; different stages; stability analysis
