The impact of sexual mixing patterns on the spread of AIDS

doi:10.1016/0025-5564(94)00073-9

Mathematical Biosciences

Volume 128, Issues 1–2, July–August 1995, Pages 211-241

https://doi.org/10.1016/0025-5564(94)00073-9 Get rights and content

Abstract

It has previously been demonstrated that the distribution of sexual partner change rates may not be sufficient behavioral information to predict the spread of AIDS. A more adequate description of the sexual network through which AIDS may spread will require information on who mixes with whom. Previous models indicated that a highly “assortive” pattern of sexual mixing, in which people of high partner change rates nearly always partner similar people, would result in a relatively rapid epidemic but one that would ultimately be rather small as it would be largely confined to those with high partner change rates. However, in earlier models it was necessary to arbitrarily vary either the partnering patterns or the distribution of partner change rates as the epidemic progressed in order to ensure consistency in the partnering patterns. Consequently, the “pure” effects of assortiveness on the size of the epidemic could not be assessed. In this paper a new model is described in which consistency in partnering patterns is maintained as the epidemic selectively depletes those with higher partner change rates. However, this model maintains consistency without arbitrary adjustments to either the assortive nature of partnering or important features of the distribution of the partner change rate. It is then possible to test the effects of assortiveness on the outcome of the epidemic without important confounding effects from the mathematical device used to maintain consistency in partnering. A practical sensitivity test on the impact of assortiveness on model predictions shows that, contrary to expectations, increasing assortiveness can, under certain circumstances, lead to larger epidemics.

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Citation Excerpt :
This failure is hard to notice because deterministic models do capture strong effects of contact patterns. In fact, these strong effects of contact patterns have been a major theme recently in the analysis of models based upon differential equations [1–26,46]. Many modelers feel that differential equation models can provide the basic insights needed to consider the effects of transmission dynamics while discrete individual models are a compromise that one must make in order to realistically model real world situations where decisions must be made with enough detail to capture all factors that should influence the decision.
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A model giving the demographic impact of AIDS is analysed to examine the sensitivity of the projections when various complicating features are included. The model deals with age and sexual partner change rate as continuous variables and uses a device to specify arbitrary correlations between the ages of the people who form sexual partnerships. The device ensures consistency, in that the amount of partner formation is the same regardless of whether the partnerships are counted from the point of view of males or females. Arbitrary correlation between partner change rate and fertility is also permitted. The results show the uncertainty in model predictions that population growth will reduce over the next 20 years to approximately zero in parts of East Africa severely affected by the AIDS epidemic. The main sources of uncertainty in the model predictions are assumptions concerning the correlation between ages in a partnership, the correlation between partner change rate and fertility, the incubation period of AIDS, and the variability of the female partner change rate.
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In this paper, we take a closer look at two harmonic mean functions [1, 2] and two minimum functions (moving dominance function [3] and group-specific minimum function), in two sex multigroup populations. Comparisons between these functions are focused on proportionate mixing. We show that under some special conditions, the two harmonic mean functions are identical; and under the mixing framework of Castillo-Chavez and Busenberg [4], the two minimum functions are also identical (for both proportionate and nonproportionate mixing). Simulations of a simple demographic model with the four functions are also performed to confirm the above mentioned identity and to illustrate the behavior of these functions.
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The impact of sexual mixing patterns on the spread of AIDS

Abstract

Math. Biosci.

Math. Biosci.

Math. Biosci.

Math. Biosci.

Math. Biosci.

Math. Comput. Modelling

Math. Biosci.

Math. Biosci.

The epidemiology of HIV infection: variable incubation plus infectious periods and heterogeneity in sexual activity

J. Roy. Stat. Soc. A

Editorial Review: mathematical and statistical studies of the epidemiology of HIV

AIDS

Epidemiological parameters of HIV transmission

Nature

The significance of sexual partner contact networks for the transmission of HIV

J. AIDS