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

ABDELATI LAGZINI; Hamid El Maroufy; Abdelkrim Merbouha; Mohamed  El Omari

doi:10.19139/soic-2310-5070-2993

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

ABDELATI LAGZINI Department of Applied Mathematics, Faculty of Science and Technology, Sultan Moulay Slimane University https://orcid.org/0009-0007-5931-3254
Hamid El Maroufy Department of Applied Mathematics, Faculty of Science and Technology, Sultan Moulay Slimane University https://orcid.org/0000-0001-6113-7543
Abdelkrim Merbouha Department of Applied Mathematics, Faculty of Science and Technology, Sultan Moulay Slimane University https://orcid.org/0009-0008-0529-9765
Mohamed El Omari Polydisciplinary faculty, Chouaib Doukkali University https://orcid.org/0000-0003-0336-9092

DOI: https://doi.org/10.19139/soic-2310-5070-2993

Keywords: SIR epidemic model, Bayesian inference, Skellam distribution, MCMC, MLE, missing data

Abstract

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.

Published

2025-12-29

How to Cite

LAGZINI, A., El Maroufy, H., Merbouha, A., & El Omari, M. (2025). Bayesian and Likelihood Inference for the SIR Model Using Skellam’s Distribution with Real Application to COVID-19. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2993

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Research Articles

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