Bayesian and Likelihood Inference for the SIR Model Using Skellam’s Distribution with Real Application to COVID-19

In this paper, we focus on the well-known SIR epidemic model, formulated as a Markov counting process with the discrete Skellam distribution. Our main objective is to estimate its key parameters, namely the infection and recovery rates. We develop a Bayesian approach that relies on Markov chain Monte Carlo and data-augmentation techniques, and establish the posterior distributions under suitable priors. We then compare the Bayesian estimators with maximum likelihood (ML) estimators, for which we study weak consistency and asymptotic normality. Finally, the theoretical results are supported with numerical simulations and illustrated through a real-world application to COVID-19 data from Morocco.