Coupled Markov switching models for spatio-temporal infectious disease counts

Spatio-temporal infectious disease counts are often subject to abrupt and dramatic changes in behavior associated with different epidemiological events. For example, a disease might go temporarily extinct in an area causing cases to drop to zero for several weeks, or an outbreak might emerge causing cases to rise rapidly. In this thesis, we propose several novel Bayesian coupled Markov switching models to account for these types of shifts in behavior. Our approach in general is to assume the disease moves between different epidemiological periods or states in each area, such as disease absence or outbreak. When the disease is in a certain state in an area, the corresponding time series follows an appropriate statistical submodel, e.g., a degenerate 0 distribution if the disease is absent or an autoregressive model with high autocorrelation if there’s an outbreak. We switch between the states through a first-order Markov chain in each area where the transition probabilities can depend on covariates and the states in neighboring areas, to account for disease spread between the areas. Inference is performed under the Bayesian paradigm, and we develop efficient Markov chain Monte Carlo methods based on jointly sampling the hidden state indicators.In the first manuscript, motivated by the abundance of spatio-temporal disease counts that contain many zeroes, we focus on models where the disease switches between periods of presence and absence in each area. Since we describe the absence state with a degenerate 0 distribution, our approach has similarities to more traditional zero-inflated models like ZIP regression. However our framework has several advantages: it naturally accounts for long periods of disease presence and absence (many consecutive zeroes); it can examine if the effects of disease spread between neighboring areas depend on certain covariates, e.g., if there is a barrier between the areas like a river; and we allow each covariate to have a separate effect on the reemergence (absence to presence) and persistence (presence to presence) of the disease, which is often epidemiologically motivated. We illustrate these advantages by comparing our model with several zero-inflated and non-zero-inflated alternatives on spatio-temporal dengue counts in Rio de Janeiro.In the second manuscript, we propose models where the disease switches between absence, endemic and outbreak periods in each area. The endemic and outbreak periods are described by autoregressive count models distinguished by a higher level of transmission during outbreaks. Markov switching models that switch between endemic and outbreak states have a long history. However, our approach has several advantages: it can account for long strings of zeroes, it allows for outbreaks in neighboring areas to affect the probabilities of outbreak emergence and persistence (along with covariates) and it prevents rapid switching between the states by enforcing minimum endemic and outbreak state durations. We apply our model, along with alternatives, to COVID-19 hospital admissions across Quebec and to simulated data where the outbreaks are known. In the third manuscript, we deal with the case of multiple diseases switching between periods of presence and absence. We are only interested in comparing the transmission dynamics of the diseases and so we assume the cases of the present diseases in an area jointly follow a multinomial distribution. Our proposal represents an interesting leap as all existing zero-inflated multinomial models have assumed independent multivariate observations. We apply the model to spatio-temporal counts of dengue, Zika and chikungunya in Rio de Janeiro. Many existing statistical models cannot account for, study, detect or forecast the abrupt and dramatic shifts in behavior often observed in spatio-temporal infectious disease counts. Therefore, this thesis represents an important contribution to the area of spatio-temporal infectious disease modeling

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