Endemic threshold results in an age-duration-structured population model for HIV infection

In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R0 for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R0 > 1, whereas it cannot if R0 < 1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R0 is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.