  The purpose of this study is to leverage modern technology (such as mobile or
web apps in Beckman et al. (2014)) to enrich epidemiology data and infer the
transmission of disease. Homogeneity related research on population level has
been intensively studied in previous work. In contrast, we develop hierarchical
Graph-Coupled Hidden Markov Models (hGCHMMs) to simultaneously track the spread
of infection in a small cell phone community and capture person-specific
infection parameters by leveraging a link prior that incorporates additional
covariates. We also reexamine the model evolution of the hGCHMM from simple
HMMs and LDA, elucidating additional flexibility and interpretability. Due to
the non-conjugacy of sparsely coupled HMMs, we design a new approximate
distribution, allowing our approach to be more applicable to other application
areas. Additionally, we investigate two common link functions, the
beta-exponential prior and sigmoid function, both of which allow the
development of a principled Bayesian hierarchical framework for disease
transmission. The results of our model allow us to predict the probability of
infection for each person on each day, and also to infer personal physical
vulnerability and the relevant association with covariates. We demonstrate our
approach experimentally on both simulation data and real epidemiological
records.
