Notes from the heterogeneous: a few observations on the implications and necessity of affinity

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.

Merging Economics and Epidemiology to Improve the Prediction and Management of Infectious Disease

“…In both variants, the key implication is that contact choices vary over time, and by health class, in response to changes in the cost of disease and disease mitigation arising from changes in the states S , I , and R . Models that focus on mixing rather than contact decisions have their roots in the affinity-based mixing models developed in the 1990s to explore the consequences of the choice of with whom to mix with, rather than how much to mix (Dietz and Hadeler 1988 ; Busenberg and Castillo-Chavez 1991 ; Hadeler and Castillo-Chavez 1995 ; Morin et al 2010 ; Galeotti and Rogers 2013 ). In such models, susceptible individuals choose P (·) rather than C (·), the value of P ( S t , I t , M t SI ) depends on the efforts susceptible individuals make to avoid mixing with infectious individuals.…”

Disease risk mitigation: The equivalence of two selective mixing strategies on aggregate contact patterns and resulting epidemic spread

“…Effort committed to avoiding risk (either in terms of contact or affinity mitigation) is implicit in the estimated parameters (see Schmitz and Castillo-Chavez (1994) and Morin et al (2010) for details). The mixing matrix, P = ( P ij ), composed of the mixing probabilities, satisfies three axioms at each moment t , (Blythe et al (1991)):…”