Spatio-temporal counts of infectious disease cases often contain an excess of zeros. Existing zero inflated Poisson models applied to such data do not adequately capture the switching of the disease between periods of presence and absence overtime. As an alternative, we develop a new zero-state coupled Markov switching Poisson 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 Poisson 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.