Parametrization of the stochastic SIRD model for covid-19 outbreak using Markov chain Monte Carlo method

• Main Authors: Muhammad Fahmi, Ahmad Zuber, Norhayati, Rosli, Noryanti, Muhammad
• Format: Conference or Workshop Item
• Language: English; English
• Published: AIP Publishing 2023
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/42343/1/8.2_Parametrization%20of%20the%20stochastic%20SIRD%20model%20for%20COVID-19%20outbreak%20using%20Markov%20Chain%20Monte%20Carlo%20method.pdf; http://umpir.ump.edu.my/id/eprint/42343/7/Parametrization%20of%20the%20Stochastic%20SIRD%20Model%20for%20COVID-19%20Outbreak.pdf; http://umpir.ump.edu.my/id/eprint/42343/; https://doi.org/10.1063/5.0152265

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. Pandemic outbreak is highly influenced by the uncontrolled factors of the 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 of the noisy behaviour 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 provide low value of the Monte-Carlo error and root mean square error (RMSE), hence indicate 1000 simulation of the MCMC provide acceptable estimated value of the epidemiological parameter for model simulation.