Dynamics of an HIV/AIDS model - The effect of time delay

In this paper an HIV/AIDS model is considered which describes the mechanics of sexual transmitted diseases. It will be shown that under some assumptions there can exist two equilibria: an infection-free state and an endemic equilibrium, and with education of the population the endemic equilibrium vanishes and the uninfected one becomes globally asymptotically stable - henceforth the disease will die out. Then in the endemic case the effect of time delay is taken into account in order to achieve a better compatibility with reality. This delay is regarded as the lag due to the evidence that time is needed during which infectious agents infect individuals of the susceptible group. Considering the delay as a bifurcation parameter the possibility of a periodic solution will be studied.