Modelling the Early Outbreak of Covid-19 Disease in Malaysia Using SIRS Model with 4-Step Adams-Bashforth-Moulton Predictor-Corrector Method

Abstract

Compartmental models have gained tremendous usage in various fields, including epidemiology, pharmacokinetics, and ecology, to describe the dynamics of a system consisting of interacting compartments one need to understand  that the challenges in using compartmental models is solving the system of ordinary differential equations (ODEs) that govern the dynamics of the compartments. In this study, we propose the use of the Adam-Bashforth predictor method to solve compartmental models formed from COVID-19 data in Malaysia between a specified period and we showcased its promising results. The Adam-Bashforth predictor method is a widely used numerical method for solving ODEs. It uses previous solution values to calculate the next solution value, and the solutions is refined by using another fashion of the formula known as ABM correction formula. We improved the performance of the Adam-Bashforth predictor method by using the first four solutions of the fourth-order Runge-Kutta method, which is another popular numerical method for solving ODEs, using the compartmental models. Our results showed that the Adam-Bashforth predictor method enhanced with the fourth-order Runge-Kutta method for accuracy and computational efficiency was able to capture the trend in the COVID-19 dataset used. Generally, the Adam-Bashforth method was about 2.5 times faster than the fourth-order Runge-Kutta method while maintaining similar accuracy. So merging two of them will in no doubt provide a better accuracy in solving the epidemiological model, the Adam-Bashforth method showed significantly accuracy, particularly in the early stages of the outbreak. The Adam-Bashforth predictor method is a promising numerical method for solving compartmental models. It offers better accuracy and computational efficiency, can be particularly useful in scenarios where accurate and fast predictions of compartmental dynamics are crucial. The model will be of great importance to the Malaysian Government, the Ministry of Health, and other stakeholders in disease management for an immediate and timely response to disease outbreaks.