Analysis of global stability of HIV/AIDS epidemic model in homogeneous community

Abstract

A model of HIV/AIDS epidemic in homogenous community is proposed and analyzed the global dynamic. The model is studied to investigate the existence of equilibria and analyze the global stability. The global dynamic is determined by the basic reproduction ratio that is obtained from the next generation matrix of the model. The endemic equilibrium point is globally asymptotically stable when this ratio exceeds unity, while the disease free equilibrium achieves the global stability when the ratio is less than unity. The simulation results are presented to simulate the evolution of population in the long term