Strategy to Computationally Model and Resolve Radioactive Decay Chain in Engineering Education by Using the Runge-Kutta Numerical Method

Balbina, F. T. C. S.; Moraes, Fernando José Habib; Munin, Egberto; Alves, Leandro Procópio

doi:10.1007/978-3-030-70601-2_339

Cited by 2 publications

(3 citation statements)

References 23 publications

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“…One apparent phenomenon about the compartmental model is that one can reasonably guess correctly the number of different compartments that Combining these parameters will lead to equation (1). Events leading to an increment of the compartment takes positive sign while those that lead to a decrease in the size of the compartment takes a negative sign.…”

Section: Model Formulationmentioning

confidence: 99%

“…Infectious disease mathematical modelling can be thought of as an intellectual representation of a physical phenomenon constructed using logic, relations, and equations to envision the perspectives Salaudeen et al / Modelling the Early Outbreak of COVID-19 Disease in Malaysia Using SIRS Model with 4-Step Adams-Bashforth-Moulton Predictor-Corrector Method 122 of an epidemic's general behaviour, opening up avenues for research into visualization of impact of specific factors on disease transmission and providing an epidemic's general behaviour as addressed by epidemic curves [1]. Additionally, it enables projections of the epidemic's longevity, infection rate, population size, and disease evaluation.…”

Section: Introductionmentioning

confidence: 99%

“…The susceptible compartment will increase based on the birth rate (  ) and recovery rate (  ) while it will decrease based on the death rate ( ) and infection rate (  ). Combining these parameters will lead to equation(1). Events leading to an increment of…”

mentioning

confidence: 99%

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

Salaudeen,

Sathasivam,

Jun Nam

et al. 2024

AMCI

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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.

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Section: Model Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%