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In epidemiological studies, zero-inflated and hurdle models are commonly usedto handle excess zeros in reported infectious disease cases. However, they cannot model the persistence (from presence to presence) and reemergence (fromabsence to presence) of a disease separately. Covariates can sometimes havedifferent effects on the reemergence and persistence of a disease. Recently, azero-inflated Markov switching negative binomial model was proposed toaccommodate this issue. We present a Markov switching negative binomial hurdlemodel as a competitor of that approach, as hurdle models are often also used asalternatives to zero-inflated models for accommodating excess zeroes. We beginthe comparison by inspecting the underlying assumptions made by both models.Hurdle models assume perfect detection of the disease cases while zero-inflatedmodels implicitly assume the case counts can be under-reported, thus weinvestigate when a negative binomial distribution can approximate the truedistribution of reported counts. A comparison of the fit of the two types ofMarkov switching models is undertaken on chikungunya cases across theneighborhoods of Rio de Janeiro. We find that, among the fitted models, theMarkov switching negative binomial zero-inflated model produces the bestpredictions and both Markov switching models produce remarkably betterpredictions than more traditional negative binomial hurdle and zero-inflatedmodels.

A Comparison between Markov Switching Zero-inflated and Hurdle Models for Spatio-temporal Infectious Disease Counts