THE ANALYSIS OF AN HIV/AIDS MODEL WITH VACCINATION

In this paper an ordinary differential equation mathematical model for the HIV/AIDS epidemic model with vaccination is presented. The dynamic of this epidemic model is analyzed, and an optional vaccine efficacy is put forward. The reproductive number, R(v), is defined, which is the number of secondary cases that one infected individual will cause through the duration of the infectious period. The disease-free equilibrium is globally asymptotically stable when R(v) < 1 and unstable when R(v) > 1. The existence of at least one endemic equilibrium point is proved for all R(v) > 1. Based on the center manifold theory, the stability of the endemic equilibrium point is given. Theoretical results show that under a planned control the number of HIV infected and AIDS individuals will be eliminated.