Inference for hidden stochastic compartmental models: application to typhoid fever dynamics in Mayotte

Abstract This study aims to estimate the parameters of a stochastic exposed–infected–removed epidemiological model for the transmission dynamics of notifiable infectious diseases. It is motivated by a data set of typhoid fever in Mayotte. The main originality and difficulty comes from the observation scheme: the only data available are periodic cumulated new retired counts. We first study the complete model to derive an analytic expression of the unknown parameters (contamination rates, incubation rate, isolation rate) as functions of some moments or some well-chosen transition probabilities. We then use the setting of hidden multi-chain Markov models and adapt the standard Baum–Welch algorithm in order to estimate the transition matrix in our hidden data framework and retrieve the parameters of interest. The performance of this approach is investigated using synthetic data, along with an analysis of the impact of employing a model with one fewer compartment to fit the data, aiding in model selection. Then, it is applied to the typhoid data set.