Solving SEIR Model Using Symmetrized Runge Kutta Methods

Abstract

During these pandemic, SEIR model has become a popular topic among researchers. Such epidemiological model is said to be a great decision tool to forecast the behaviour of Covid19 outbreak for future actions. Following trend, this paper attempts to use symmetrized Runge Kutta methods; Implicit Midpoint Rule (IMR) and Implicit Trapezoidal Rule (ITR), to solve this model. The base method; IMR and ITR are tested with one-step symmetrization (1ASIMR, 1ASITR, 1PSIMR, and 1PSITR) and two-step symmetrization (2ASIMR, 2ASITR, 2PSIMR and 2PSITR) in both active and passive modes. Symmetrized Runge-Kutta method is best when using along stiff equations. Thus, we used high rate of disease transmission, β to study the efficiency of each method and predict the proportion of individuals in each category according to the SEIR model. All the parameters and values are obtained through official websites of Malaysia and calculated based on previous studies starting from 2 nd December 2021 to 1st January 2022. The equilibrium points: disease free equilibrium (DFE) and the disease endemic equilibrium (DEE) are presented and calculated. Next, the basic reproduction number, R 0 is computed using the next generation method. The result depicted R 0 > 1, which indicates the disease has spread over. Finally, 2PSIMR is found to be the best method out of all. The efficiency of the methods is discussed and compared.