A stochastic point process model of the incubation period of a HIV infected individual

Abstract

The inability to get people to regularly test and know their HIV status has caused the widespread unavailability of correct and comprehensive data on HIV infection especially the time at which an individual was first infected. Hence, mathematical scientists have relied extensively on inference obtained from small samples to estimate the HIV incubation and seroconversion times. We set out to obtain in this paper, (i) the distribution functions of the HIV incubation period and seroconversion time by considering the stochastic behaviours of the members of the population under discussion, and (ii) the method of estimation that gives the best parameter estimate by building on previous work of Lui et al. (1988) and Medley et al. (1988). We obtained a one-parameter family distribution for the incubation period and a two-parameter family distribution for the seroconversion time. Data on homosexual individuals were used since we built on past work of Lui et al. (1988). Also AIDS incidence projection was done using the backcalculation method. However, the shortfall of the back-calculation method was not addressed in this paper as this is meant for further research.