Forward projection of HIV prevalence [letter]

As an economist writing to an august medical journal. I feel like the proverbial fool. However the subject is too serious for angelic circumspection. May I refer to the article by Shapiro et al. on the screening of antenatal blood samples for antibodies to HIV. In the conclusion the authors shrank back from the abyss of the disaster implicit in their forward extrapolations. On the basis of the conservative doubling time of 6 months they projected the incidence among black pregnant women in this geographical area to be in excess of 1% by the end of 1989 and approximately 6% by the end of 1990 unless urgent and vigorous steps were taken to inhibit the spread of the disease. The logical further extrapolation gives a total 100% incidence on a conservative basis by the 1st quarter of 1993; and a year earlier if confirmed and unconfirmed screen-positive results are extrapolated. These horrendous results would appear to me to turn on the implicit growth formula of: p=po.exp(gt) where p is the proportion of infected women g the exponential growth factor and t time. The trouble is that this is an unbounded function and must quickly exceed unity if the growth rate is assumed to remain high. An alternative formulation would be the following: p=po+(1-po).exp(-a/t) where a is the exponential parameter. The advantage of this formulation is that the exponential element is confined to a range of values of 0-1 and means that total incidence is reached asymptotically at infinity. This formulation fitted to the findings results in the following projections of % incidence (see chart). Still horrendous but the results show that marked extrapolation differences dependent on the choice of underlying growth formula. (full text)