Parametrization of the stochastic SIRD model for COVID-19 outbreak using Markov Chain Monte Carlo method

The susceptible-infectious-recover-death SIRD deterministic compartmental model is the most frequent mathematical model of the epidemic outbreak. The model consists of four states, susceptible, infected, recovered, and death. The pandemic outbreak is highly influenced by the uncontrolled factors of environmental noise. This paper is at aimed to extend the deterministic model of SIRD to a stochastic SIRD counterpart. The epidemiological parameters are perturbed with the noisy behavior of the Wiener process to gain insight into the noisy behavior of the outbreak. The parameters representing the rate between the four states (infection rate, recovery rate, fatality rate, and immune lost rate) are estimated using the Markov Chain Monte Carlo (MCMC) method using 200, 400, and 1000 simulations. The result shows that as the number of sample paths is increased (1000 simulations), the parameter estimated from the model provides a low value of the Monte-Carlo error and root mean square error (RMSE), hence indicating 1000 simulation of the MCMC provide the acceptable estimated value of the epidemiological parameter for model simulation.