  We consider a time-delayed HIV/AIDS epidemic model with education
dissemination and study the asymptotic dynamics of solutions as well as the
asymptotic behavior of the endemic equilibrium with respect to the amount of
information disseminated about the disease. Under appropriate assumptions on
the infection rates, we show that if the basic reproduction number is less than
or equal to one, then the disease will be eradicated in the long run and any
solution to the Cauchy problem converges to the unique disease-free equilibrium
of the model. On the other hand, when the basic reproduction number is greater
than one, we prove that the disease will be permanent but its impact on the
population can be significantly minimized as the amount of education
dissemination increases. In particular, under appropriate hypothesis on the
model parameters, we establish that the size of the component of the infected
population of the endemic equilibrium decreases linearly as a function of the
amount of information disseminated. We also fit our model to a set of data on
HIV/AIDS from Uganda within the period 1992-2005 in order to estimate the
infection, effective response, and information rates of the disease. We then
use these estimates to present numerical simulations to illustrate our
theoretical findings.
