Abstract
A population is divided into three age-groups: 0- a 1, a 1- a 2, and a 2 and more years. It is the third group that is sexually mature and active and, therefore, capable of reproduction. It is also this group that is responsible for the horizontal transmission of the epidemic through heterosexual activities and for vertical transmission to the first group by infected mothers. It is shown that, in the third group, the HIV prevalence is an increasing function of time and it is bounded by two logistic functions over the time interval [0, 2 a 2] years. The equations of the model are delayed differential equations. The method of steps is used in obtaining the bounding functions for the HIV prevalence. The effects of medical and/or social intervention is discussed in relation to the epidemiological parameters: infectiveness β, the rate of acquiring new sexual partners c, and the incubation period D= 1 υ 3 .
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