COVID-19 epidemic model: study of numerical methods and solving optimal control problem through forward-backward sweep method

Abstract

COVID-19 pandemic is still a great challenge for several research fields. A mathematical model is one of the main epidemiology research contributions, which is able to study the pattern of disease spread and its long-term behavior. Many researchers have done this research with their interventions and mathematical approach methods, such as model analysis, use of optimal control theory, data used and numerical methods for solving the model. In this paper, we normalize the basic SIR epidemiological model and estimate the parameters involved based on the COVID-19 data in Indonesia, especially for West Java. The optimal control theory is applied to know the disease behavior by considering vaccination and its cost to prevent the spread of the disease. To see the disease behavior through graphical simulation, the Runge-Kutta Fehlberg method is used for solving the model numerically. The result shows that the spread of COVID-19 can be prevented and controlled due to vaccination.