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Abstract
Hidden Markov Models (HMMs) are suitable statistical method for explaining serial dependency in time series data. As per the model, observations are generated from a finite mixture of distributions governed by the principle of Markov chain. Here, we consider Zero Inflated Poisson-Hidden Markov Model (ZIP-HMM) for the series of monthly cholera count data in Kerala during the 2006-2018 period. Cholera is an infectious disease contracted by the consumption of food or water contaminated with Vibrio Cholerae (VC) bacteria. For this analysis, the parameters are estimated by Expectation Maximization(EM) technique. Here, a two-state ZIP-HMM is found to be the better model using Akaike information criterion(AIC) andBayesian information criterion(BIC). The 'absence' and 'presence' of the VC bacteria are the two hidden states of the fitted model. The best sequence of these hidden states was obtained using Viterbi algorithm.