  Recurrent COVID-19 outbreaks have placed immense strain on the hospital
system in Quebec. We develop a Bayesian three-state coupled Markov switching
model to analyze COVID-19 outbreaks across Quebec based on admissions in the 30
largest hospitals. Within each catchment area, we assume the existence of three
states for the disease: absence, a new state meant to account for many zeroes
in some of the smaller areas, endemic and outbreak. Then we assume the disease
switches between the three states in each area through a series of coupled
nonhomogeneous hidden Markov chains. Unlike previous approaches, the transition
probabilities may depend on covariates and the occurrence of outbreaks in
neighboring areas, to account for geographical outbreak spread. Additionally,
to prevent rapid switching between endemic and outbreak periods we introduce
clone states into the model which enforce minimum endemic and outbreak
durations. We make some interesting findings, such as that mobility in retail
and recreation venues had a positive association with the development and
persistence of new COVID-19 outbreaks in Quebec. Based on model comparison our
contributions show promise in improving state estimation retrospectively and in
real-time, especially when there are smaller areas and highly spatially
synchronized outbreaks. Furthermore, our approach offers new and interesting
epidemiological interpretations, such as being able to estimate the effect of
covariates on disease extinction.
