Empirical methods for the estimation of the mixing probabilities for socially structured populations from a single survey sample.
ABSTRACT "The role of variability of sexual behavior in the transmission dynamics of HIV and AIDS has been illustrated, through the use of mathematical models, by several investigators.... In this paper we describe some practical methods for estimating the deviations from random mixing from a single survey sample.... We include a description of the role of the estimated mixing probabilities in models for the spread of HIV, a discussion of alternatives and possible extensions of the methods described in this article, and an outline of future directions of research." (SUMMARY IN FRE)
- SourceAvailable from: Carlos Castillo-Chávez[Show abstract] [Hide abstract]
ABSTRACT: A central aspect in the study of the dynamics of sexually transmitted diseases is that of mixing. The study of the effects of social structure in disease dynamics has received considerable attention over the last few years as a result of the AIDS epidemic. In this paper, we formulate a generalization of the Blythe and Castillo-Chavez social/sexual framework for human interactions through the incorporation of age structure, and derive an explicit expression in terms of a preference function for the general solution to this formulation. We emphasize the role played by proportionate mixing, the only separable solution to this mixing framework, through the discussion of several specific cases, and we formulate an age-structured epidemic model for a single sexually active homosexual population, stratified by risk and age, with arbitrary risk- and age-dependent mixing as well as variable infectivity. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductivIMA journal of mathematics applied in medicine and biology 02/1991; 8(1):1-29.
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ABSTRACT: Sexually transmitted diseases such as gonorrhea, syphilis, herpes, and AIDS are driven and maintained in populations by epidemiological and sociological factors that are not completely understood. One such factor is the way in which people mix sexually. In this paper, we outline a unified approach to modeling sexual mixing structures, where such structures are defined in terms of a set of axioms for a finite number of distinct groups of people. Theorems for homosexual, heterosexual, and arbitrary group mixing are presented, leading to a representation of all mixing structures defined by the axioms. The representation and its parameters are interpreted in terms of intergroup affinities for sexual mixing. The use of the approach in sexually transmitted disease modeling is discussed.Mathematical Biosciences 01/1992; 107(2):379-405. · 1.45 Impact Factor
Article: Affinity in paired event probability[Show abstract] [Hide abstract]
ABSTRACT: It is shown that a general parametric functional generates the conditional and joint probabilities of event pairs when the order within paired events is irrelevant. The parameters represent affinities or associations between single events. If the marginal probabilities of the single events are known, then these parameters specify a hypersurface on which all the joint probabilities of event pairs must lie. Examples are presented, and applications in probability, ecology, epidemiology, genetics, and distribution theory are offered.Mathematical Biosciences 01/1995; 128(1-2):265-284. · 1.45 Impact Factor