Sex, drugs and matrices: Mathematical prediction of HIV infection

Abstract

The purpose of this paper is to consider a very simple model of the AIDS epidemic. This model illustrates how the spread of AIDS can be affected by parameters whose values, at the present time, are very imprecise or unknown. Of particular interest are the data related to sexual encounters and practices, data which are often unreliable or ambiguous. In this regard, the present model also suggests that the epidemiology of AIDS is particularly sensitive to the limitations in the assessment of sexuality/drug‐related behavior. Using a system of elementary differential equations, the present paper illustrates (using 3 examples) that depending upon the value of critical parameters, one could predict either very rapid increases of seropositivity or a decreasing rate of seropositivi‐ty. Thus, in order to diminish the ambiguity, it becomes crucial to make careful estimates of the sexual “interaction” coefficients, along with all other parameters, to insure that reasonable predictions can be made.