An Efficient Numerical Simulation for the Fractional COVID-19 Model Using the GRK4M Together with the Fractional FDM

Abstract

In this research, we studied a mathematical model formulated with six fractional differential equations to characterize a COVID-19 outbreak. For the past two years, the disease transmission has been increasing all over the world. We included the considerations of people with infections who were both asymptomatic and symptomatic as well as the fact that an individual who has been exposed is either quarantined or moved to one of the diseased classes, with the chance that a susceptible individual could also migrate to the quarantined class. The suggested model is solved numerically by implementing the generalized Runge–Kutta method of the fourth order (GRK4M). We discuss the stability analysis of the GRK4M as a general study. The acquired findings are compared with those obtained using the fractional finite difference method (FDM), where we used the Grünwald–Letnikov approach to discretize the fractional differentiation operator. The FDM is mostly reliant on correctly converting the suggested model into a system of algebraic equations. By applying the proposed methods, the numerical results reveal that these methods are straightforward to apply and computationally very effective at presenting a numerical simulation of the behavior of all components of the model under study.

Keywords

• COVID-19
• generalized RK4 method
• fractional FDM
• Grünwald–Letnikov’s approach
• stability analysis