Possible demographic consequences of HIV/AIDS epidemics. II: Assuming HIV infection does not necessarily lead to AIDS.

*(English)*Zbl 0697.92018
Mathematical approaches to problems in resource management and epidemiology, Proc. Conf., Ithaca/NY (USA) 1987, Lect. Notes Biomath. 81, 220-248 (1989).

[For the entire collection see Zbl 0682.00021.]

In the first part, Math. Biosci. 90, No.1/2, 475-505 (1988; Zbl 0673.92008), the authors studied the case where HIV infection always develops into AIDS. In this second part they adopt the hypothesis that HIV infection does not necessarily lead to AIDS. The main objective is on the interplay between epidemiological and demographic effects. The model is a set of first order differential equations, the population is divided into three groups: susceptibles, infected (infectious) and those who were infectious but no longer are, that is the “recovered class”. The study is for heterosexual transmission of HIV. The authors assume that contacts occur homogeneously over all age groups. It contains as a special case the one studied in part I.

Phase plane analysis and asymptotic behaviour is carried out for some numerical cases. The model is then extended to an age-structured population, and an asymptotic study is carried out. The results are then reviewed as to their population effects, with conclusions in terms of population growth and the “child dependency ratio”. An appendix solves some apparent inconsistencies that were not fully explained in part I.

In the first part, Math. Biosci. 90, No.1/2, 475-505 (1988; Zbl 0673.92008), the authors studied the case where HIV infection always develops into AIDS. In this second part they adopt the hypothesis that HIV infection does not necessarily lead to AIDS. The main objective is on the interplay between epidemiological and demographic effects. The model is a set of first order differential equations, the population is divided into three groups: susceptibles, infected (infectious) and those who were infectious but no longer are, that is the “recovered class”. The study is for heterosexual transmission of HIV. The authors assume that contacts occur homogeneously over all age groups. It contains as a special case the one studied in part I.

Phase plane analysis and asymptotic behaviour is carried out for some numerical cases. The model is then extended to an age-structured population, and an asymptotic study is carried out. The results are then reviewed as to their population effects, with conclusions in terms of population growth and the “child dependency ratio”. An appendix solves some apparent inconsistencies that were not fully explained in part I.

Reviewer: H.de Arazoza

##### MSC:

92D25 | Population dynamics (general) |