Projecting social contact matrices to populations stratified by binary attributes with known homophily

Claus Kadelka; Claus Kadelka

doi:10.3934/mbe.2023154

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3282-3300. doi: 10.3934/mbe.2023154

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Projecting social contact matrices to populations stratified by binary attributes with known homophily

Claus Kadelka ^,

Department of Mathematics, Iowa State University, 411 Morrill Rd, Ames, IA 50011, USA

Received: 24 August 2022 Revised: 16 November 2022 Accepted: 27 November 2022 Published: 05 December 2022

Contact networks are heterogeneous. People with similar characteristics are more likely to interact, a phenomenon called assortative mixing or homophily. Empirical age-stratified social contact matrices have been derived by extensive survey work. We lack however similar empirical studies that provide social contact matrices for a population stratified by attributes beyond age, such as gender, sexual orientation, or ethnicity. Accounting for heterogeneities with respect to these attributes can have a profound effect on model dynamics. Here, we introduce a new method, which uses linear algebra and non-linear optimization, to expand a given contact matrix to populations stratified by binary attributes with a known level of homophily. Using a standard epidemiological model, we highlight the effect homophily can have on model dynamics, and conclude by briefly describing more complicated extensions. The available Python source code enables any modeler to account for the presence of homophily with respect to binary attributes in contact patterns, ultimately yielding more accurate predictive models.
- infectious disease modeling,
- mathematical epidemiology,
- homophily,
- assortative mixing,
- heterogeneity,
- contact networks,
- contact patterns
Citation: Claus Kadelka. Projecting social contact matrices to populations stratified by binary attributes with known homophily[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3282-3300. doi: 10.3934/mbe.2023154

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Abstract

Contact networks are heterogeneous. People with similar characteristics are more likely to interact, a phenomenon called assortative mixing or homophily. Empirical age-stratified social contact matrices have been derived by extensive survey work. We lack however similar empirical studies that provide social contact matrices for a population stratified by attributes beyond age, such as gender, sexual orientation, or ethnicity. Accounting for heterogeneities with respect to these attributes can have a profound effect on model dynamics. Here, we introduce a new method, which uses linear algebra and non-linear optimization, to expand a given contact matrix to populations stratified by binary attributes with a known level of homophily. Using a standard epidemiological model, we highlight the effect homophily can have on model dynamics, and conclude by briefly describing more complicated extensions. The available Python source code enables any modeler to account for the presence of homophily with respect to binary attributes in contact patterns, ultimately yielding more accurate predictive models.

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