How May Infection-Age-Dependent Infectivity Affect the Dynamics of HIV/AIDS?

Epidemiological and behavioral factors crucial to the dynamics of HIV/AIDS include long and variable periods of infectiousness, variable infectivity, and the processes of pair formation and dissolution. Most of the recent mathematical work on AIDS models has concentrated on the effects of long periods of incubation and heterogeneous mixing in the transmission dynamics of HIV. This paper explores the role of variable infectivity in combination with a variable incubation period in the dynamics of HIV transmission in a homogeneously mixing population. 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 Ro and show that the disease dies out if {\$}R{\_}0 < 1{\$}, whereas if {\$}R{\_}0 > 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.