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“The only thing necessary for these diseases to the triumph is for good people and governments to do nothing.”

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ADDENDUM TO ASSA600: AN AIDS MODEL OF THE THIRD KIND?

R E Dorrington BA, BCom, BSc (Hons), MPhil, ASA, FIA

ABSTRACT

 

This addendum outlines changes made to the ASSA AIDS model since the abovementioned paper was published.  These changes were necessitated by the release of the 1996 Census results and an "AIDS Experts" workshop organised by the Department of Health, but the opportunity was also used to implement a number of improvements to the model.

KEYWORDS

AIDS, modelling, population, census, fertility, mortality, migration, South Africa.

 1. INTRODUCTION

Since the above paper was published before, inter alia, the release of the 1996 Census results and an "AIDS Experts" workshop organised by the Department of Health it does not describe the changes made to the model to incorporate insights that resulted from these sources of data.  It is the purpose of this addendum to document the changes to the model made since the publication of the original paper.

2. STARTING POPULATION

The starting population was derived in the same way as before.  However as the assumptions of mortality, fertility and migration have changed, as described below this resulted in a slightly lower starting population than in the original paper (32,8 million instead of 33,1 million).

3. FERTILITY

HIV-negative fertility

Fertility rates up to 1992 were re-estimated in the light of the Census results.  In particular it was decided to apply the TFR projection model outlined in the paper only from 1993 onwards.  TFRs for the years before this were estimated as follows.  First Gompertz’s standard fertility curve was fitted to Sadie’s ASFRs in order to smooth some particularly high rates.  The TFRs were then set to the average of Sadie's adjusted TFRs and those implied by Udjo's projections (Udjo, 1998) on the basis of Sadie's adjusted ASFRs(1)  As TFRs were estimated only for five-yearly periods, TFRs for individual years were interpolated from polynomials of degree 3 fit to 1967.5-1977.5, 1972.5-1982.5 and 1982.5-1992.5 (2) and for individual ages using the Gompertz standard distribution

As the original method of determining ASFRs in the future produced negative rates at some ages when the TFR fell below 1,5 (i.e. some 60 years into the future) it was decided to alter the method.  Now the model produces ASFRs from a standard two-parameter Gompertz curve (with the two parameters changing with TFR to maintain a realistic shape).  In addition the user can set the limit below which the TFR will not fall.

HIV-positive fertility

As mentioned in the paper ideally it is necessary to model the ratio of HIV-positive fertility to HIV-negative fertility taking into account duration since becoming infected.  This was not done in the earlier version of the model resulting in an exaggeration of the impact of the epidemic on fertility.

This has been remedied in the final version by arbitrarily (3) setting the ratio of those who have been infected for t years to be equal to:

where

is the ratio of fertility rates of those at age x who become infected to those who do not just before being infected (assumed to be close to the age specific ratios assumed by Zaba and Gregson (1998) for ages below 20, and one thereafter).