  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.
