AIDS Epidemiology pp 384-402 | Cite as

# On the Estimation Problem of Mixing/Pair Formation Matrices with Applications to Models for Sexually-Transmitted Diseases

## Abstract

A problem of considerable importance lying at the interface of social dynamics, demography, and epidemiology is determining and modeling who is mixing with whom. In this article we describe a general approach, using nonlinear mixing matrices, for modeling the process of pair-formation in heterogeneous populations. Determining who is mixing with whom is complicated by a variety of factors, including the problem of denominators, which is, in our context, equivalent to the nonexistence of closely interacting social/sexual networks. We describe the use of a mark-recapture model for estimating the sizes of the missing link, that is, the size of the population having sexual contact with a specified population and hence at risk for sexually-transmitted diseases. The need to estimate the size of the sexually-active subset before estimating the size of the population at risk introduces extra variability into the problem. An estimator of the variance of the estimated size of the population at risk that accounts for this extra variability and an expression for the bias of such an estimator have been derived. We illustrate our results with data collected from a population of university undergraduates, and make use of our axiomatic modeling approach for mixing/pair formation to compute specific mixing matrices. Complete details of this work will be published elsewhere.

## Keywords

Human Immunodeficiency Virus Sexual Partner Formation Matrice Sexual Contact Transmission Dynamic## Preview

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## References

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