Simplified Modelling of the Population Dynamics of HIV/AIDS

Abstract

Scherrer et al. (1985) demonstrated a simplified approach to the modelling of the spatial spread of influenza from an initial focus. Results for the Leningrad outbreak of 1965 confirmed previous Soviet claims to be able to predict the spread to other centres in the USSR and also justified the approximations made. Instead of adopting complex assumptions about the frequency distribution of the infectious period, it was simply supposed that the latter followed a negative exponential distribution with parameters to be estimated from the data. Again, instead of attempting to deal with an intricate transportation network, for which most flows were not available, cities which had a clearly identified major link with Leningrad were selected. Encouraged by this work, admittedly carried out 20 years after the events in question, Bailey and Estreicher (1986) proposed the adoption of a similar approach to the ongoing epidemic of AIDS. They explicitly recognised that it would be necessary to develop methods, inevitably based on inadequate data, that could be understood and be used by decision makers to act more effectively immediately. While not denying the existence of heterogeneity, it was assumed that for practical purposes a large number of variable factors would have an overall average effect in large populations that could be adequately described by a simple model with only a few parameters. This worked for influenza, but will it also work for AIDS? The subject is very complicated: see Anderson et al. (1986), May and Anderson (1987) and Isham (1988) for excellent broad reviews and references to current work. Several serious difficulties arise in attempts at simplification. First, there are very wide variations in human sexual behaviour. Secondly, the incubation period is long and variable with an average value of several years. Available data show considerable skewing to the right, but this is just the area which is subject to truncation. Thirdly, there is much uncertainty about the proportion of HIV positives who will ultimately develop AIDS. Fourthly, as data and information increase the whole situation becomes more complex rather than less. The paradox is that we shall be able to do the work properly only when it is too late to be useful. In the meantime, ministers of health continue to make decisions which have far reaching consequences.