Bayesian Inference for SIS Type Epidemic Model by Skellam’s Distribution with Real Application to COVID-19

In this paper, we present a simple SIS epidemic to understand the dynamics of COVID-19 in a homogeneous and closed population. We formulate the model using the Markov process characterized by Skellam’s distribution. We investigate the Bayesian inference to estimate the key model parameters, especially the reproduction number. The estimation was carried out by augmenting the low-frequency observations by simulation of latent data points between two pair of real observations, which involves imputing the missing data in addition to the model parameters. We develop Markov chain Monte Carlo (MCMC) algorithm methods to explore the posterior distribution of the parameters and missing data. We support findings by numerical simulations and we apply the methodology to real-world Data from COVID-19 in Morocco.