We explore the use of Poisson-hidden Markov model to describe an overdispersed data on monthly death counts due to Dengue fever. Independent Poisson mixture models of various components and stationary Poisson hidden Markov models of different states are fitted and the performance of each model is judged using model selection criteria. The sequence of hidden states are estimated based on the best fitted model. The method can be applied in identifying environmental factors affecting a stochastic process.