Article

Empirical methods for the estimation of the mixing probabilities for socially-structured populations from a single survey sample

ENGLAND
Mathematical Population Studies (Impact Factor: 0.29). 02/1992; 3(3):199-225, 227. DOI: 10.1080/08898489209525339
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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)

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    • "It was also shown that solutions P to the mixing axioms can be characterized as multiplicative perturbations of proportionate mixing, the unique separable solution. In fact, it was shown that (for alternative recently result [25]): Theorem 2.1 : ([5] [6] [8] [9]) All matrices P ij satisfying the above mixing axioms can be generated as multiplicative perturbations of proportionate mixing via the " preference " symmetric matrix Φ. "
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    ABSTRACT: The problem of who is mixing with whom is of great theoretical importance in the context of heterosexual mixing. In this article, we publish for the first time, data from a study carried out in 1989 that had the goal of estimating who is mixing with whom, in heterosexually active college populations in the presence of co-factors like drinking. The gathering of these data and the challenges involved in modelling the interaction between and among heterosexually active populations of individuals are highlighted in this manuscript. The modelling is based on the assumptions that at least two processes are involved: individual affinities or preferences determine 'what we want' while mixing patterns describe 'what we get'. We revisit past results on the role of affinity/preference on observed mixing patterns in one- and two-sex mixing populations. Some new results for homosexually active populations are presented. The study of mixing is but the means to an end and consequently, we also look at the role of affinity on epidemics as filtered by observed mixing patterns. It would not be surprising to observe that highly distinct preference or mixing structures may actually lead to quite similar epidemic patterns.
    Full-text · Article · Sep 2010 · Journal of Biological Dynamics
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    • "Recently, we have also estimated the contact structure, as modeled by our mixing matrices, of a student population as a function of sexual or dating activity (see Castillo-Chavez et al., 1992; Hsu Schmitz and Castillo-Chavez, 1992). In addition, we have worked on methods for estimating the parameters associated with arbitrary mixing structures (see Rubin et al., 1991; Blythe et al., 1992). Furthermore, the representation theory of mixing matrices as a function of the preference structure of a population, as first developed by Busenberg and Castillo-Chavez (1989, 1991), has allowed us to begin studying the role of preference in two-sex mixing populations (see Hsu and Castillo-Chavez; Hsu et al., 1993). "
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    ABSTRACT: The transmission of diseases, genetic characteristics, or cultural traits is influenced by many factors including the contact/social structure of the interacting subpopulation, that is, the social environment. Classical demography (see MacKendrick, 1926; Lotka, 1922; and Leslie, 1945) ignores social dynamics and usually concentrates on the birth and death processes of female populations under the assumption that they have reached a stable age distribution. They usually ignore the specific mating/contact structure of the population. The incorporation of mating structures or marriage functions, as they are commonly referred to in human demography, was pioneered by Kendall (1949) and Keyfitz (1949). However, despite the fact that their work was extended by Parlett (1972), Predrickson (1971), McFarland (1972), and Pollard (1973) two decades ago, their impact on demography, epidemiology, and population biology has been minimal.
    Full-text · Chapter · Jun 1994
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    • "Recently, we have also estimated the contact structure, as modeled by our mixing matrices, of a student population as a function of sexual or dating activity (see Castillo-Chavez et al., 1992; Hsu Schmitz and Castillo-Chavez, 1992). In addition, we have worked on methods for estimating the parameters associated with arbitrary mixing structures (see Rubin et al., 1991; Blythe et al., 1992). Furthermore, the representation theory of mixing matrices as a function of the preference structure of a population, as first developed by Busenberg and Castillo-Chavez (1989, 1991), has allowed us to begin studying the role of preference in two-sex mixing populations (see Hsu and Castillo-Chavez; Hsu et al., 1993). "
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    ABSTRACT: Abstract. Social dynamics have had a strong impact on the development of theoretical epidemiology over the last six years. Interactions or contacts among individuals have traditionally been modeled by the use of the mass-action law or proportionate mixing, giving limited understanding of ...
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