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.

翻译：社会接触矩阵是传染病流行病学中的核心工具，因为它们量化了直接驱动空气传播传染病传播的近距离人际接触模式。本文提出一个贝叶斯建模框架，用于推断在传统年龄维度之外进行分层的广义接触矩阵。该模型旨在满足接触的基本结构假设，同时利用张量结构与平滑约束，使高维矩阵估计具备计算可行性与统计稳定性。我们发现，在结构约束下进行多维矩阵分层与列联表理论之间存在联系。这使得我们能够处理实际数据分析中常见的具有挑战性的缺失数据问题——接触对象特征信息未被观测的情况。通过模拟研究，我们将该框架与现有方法进行基准对比，并利用两个真实世界数据集（美国BICS和德国COVIMOD）说明其实用性。我们的模型已实现为开源Python包，以促进其在更广泛的科学界的应用。