How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?

The authors keep track of an individual's infection-age, that is, the time that has passed since infection, and assume a nonlinear functional relationship between mean sexual activity and the size of the sexually active population that saturates at high population sizes. The authors identify a basic reproductive number R_o and show that the disease dies out if R_o < 1, whereas if R_o > 1 the disease persists in the population, and the incidence rate converges to or oscillates around a uniquely determined nontrivial equilibrium. Though conditions are found for the endemic equilibrium to be locally asymptotically stable, undamped oscillations cannot be excluded in general and may occur in particular if the variable infectivity is highly concentrated at certain parts of the incubation period. Whether undamped oscillations can also occur for the reported one early peak and one late plateau of infectivity observed in HIV-infected individuals must be a subject of future numerical investigations.