Spatio-temporal counts of infectious disease cases often contain an excess of zeros. With existing zero inflated count models applied to such data it is difficult to quantify space-time heterogeneity in the effects of disease spread between areas. Also, existing methods do not allow for separate dynamics to affect the reemergence and persistence of the disease. As an alternative, we develop a new zero-state coupled Markov switching negative binomial model, under which the disease switches between periods of presence and absence in each area through a series of partially hidden nonhomogeneous Markov chains coupled between neighboring locations. When the disease is present, an autoregressive negative binomial model generates the cases with a possible 0 representing the disease being undetected. Bayesian inference and prediction is illustrated using spatio-temporal counts of dengue fever cases in Rio de Janeiro, Brazil.