Bayesian Modeling and Prediction of Generalized Contact Matrices

2026-05-07

AI Summary

Traditional social contact matrices, stratified solely by age, struggle to capture high-dimensional heterogeneous contact patterns and exhibit limitations when attribute information is missing. This work proposes a Bayesian tensor modeling framework that, for the first time, integrates multidimensionally stratified contact matrices with contingency table theory. By incorporating structured priors, tensor decomposition, and smoothing regularization, the method yields robust estimates of high-dimensional generalized contact matrices while respecting epidemiological constraints such as reciprocity. It effectively handles missing data and demonstrates significant performance gains over existing benchmarks on real-world datasets—BICS (United States) and COVIMOD (Germany). An accompanying open-source Python package is provided to facilitate community adoption and application.

Abstract

Social contact matrices are essential tools in infectious disease epidemiology as they quantify close-range human contact patterns which directly drive the transmission of airborne infectious diseases. In this work we propose a Bayesian modeling framework for inferring generalized contact matrices which stratify contact matrices beyond contemporary age dimensions. The model is designed to satisfy fundamental structural assumptions of contacts while leveraging tensor structures and smoothing constraints to make high-dimensional matrix estimation computationally feasible and statistically stable. We discover a link between multi-dimensional matrix stratification subject to structural constraints with the theory of contingency tables. This enables us to approach a challenging missing-data problem commonly encountered in real-world analysis where feature information on the contacts is unobserved. We benchmark the framework against existing methods through simulation studies and illustrate the framework's practical utility through two real-world datasets: BICS (United States) and COVIMOD (Germany). Our models are implemented in an open-source Python package to facilitate adoption in the wider scientific community.

Problem

• contact matrices
• infectious disease epidemiology
• missing data
• high-dimensional estimation
• human contact patterns

Innovation

• Bayesian modeling
• generalized contact matrices
• tensor smoothing
• contingency tables
• missing data imputation