Hidden Markov Individual-level Models of Infectious Disease Transmission

Music City Center 

Individual-level models of infectious disease transmission are being increasingly used to help understand the transmission dynamics of various diseases. However, fitting such models to individual-level epidemic data is challenging, as we often only know when an individual was detected and not when they were infected or removed. To account for missing infection and removal times, we first assume the epidemiological states of the individuals (e.g., susceptible, infectious, or recovered) follow a series of hidden coupled first-order Markov chains. The observed detection times are then generated conditional on the states of the chains using autoregressive Bernoulli models. Bayesian coupled hidden Markov models have been used for individual-level epidemic data before. However, these approaches assumed each individual was continuously tested and that the tests were independent. Often, individuals are only tested until their first positive test, and multiple tests on the same individual might not be independent. We accommodate these scenarios by assuming the probability of detecting the disease can depend on past observations, which allows us to fit a much wider range of practical applications. Our approach only requires the initial detection time of each detected individual. Also, unlike more traditional data augmentation methods, we do not assume this detection time corresponds to infection or removal or that infected individuals must at some point be detected. We illustrate the flexibility of our approach by fitting two examples: an experiment on the spread of tomato spot wilt virus in pepper plants and an outbreak of norovirus among nurses in a hospital. All models are fit under a unified Bayesian framework using the individual forward filtering backward sampling algorithm implemented with NIMBLE's custom sampler feature.