Individual-level epidemic models are increasingly being used to help understand the transmission dynamics of various infectious diseases. However, fitting such models to individual-level epidemic data is challenging, as we often only know when an individual first showed symptoms of the disease and not when they were infected or removed. We propose an autoregressive coupled hidden Markov model to infer unknown infection and removal times, as well as other model parameters, given only the symptom-onset times. More traditional data augmentation methods used in epidemic modelling have either assumed that the infection or removal times are known or that all infected individuals showed symptoms. In contrast, we build an observation model where there is a chance that an infectious individual never shows symptoms during the study, allowing for undetected (e.g., asymptomatic) infections. Symptom onset is not assumed to correspond to infection or removal. Bayesian coupled hidden Markov models have been used previously for individual-level epidemic data consisting of laboratory diagnostic test results. However, these models are not appropriate for symptom-onset data, as they have a chance of generating multiple symptom-onset times for an individual. In contrast, we incorporate autoregression into the observation process, ensuring that at most one symptom-onset time is observed per individual. 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.

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