A higher order Galerkin time discretization scheme for the novel mathematical model of COVID-19

Abstract

In the present period, a new fast-spreading pandemic disease, officially recognised Coronavirus disease 2019 (COVID-19), has emerged as a serious international threat. We establish a novel mathematical model consists of a system of differential equations representing the population dynamics of susceptible, healthy, infected, quarantined, and recovered individuals. Applying the next generation technique, examine the boundedness, local and global behavior of equilibria, and the threshold quantity. Find the basic reproduction number $R_0$ and discuss the stability analysis of the model. The findings indicate that disease fee equilibria (DFE) are locally asymptotically stable when $R_0 < 1$ and unstable in case $R_0 > 1$. The partial rank correlation coefficient approach (PRCC) is used for sensitivity analysis of the basic reproduction number in order to determine the most important parameter for controlling the threshold values of the model. The linearization and Lyapunov function theories are utilized to identify the conditions for stability analysis. Moreover, solve the model numerically using the well known continuous Galerkin Petrov time discretization scheme. This method is of order 3 in the whole-time interval and shows super convergence of order 4 in the discrete time point. To examine the validity and reliability of the mentioned scheme, solve the model using the classical fourth-order Runge-Kutta technique. The comparison demonstrates the substantial consistency and agreement between the Galerkin-scheme and RK4-scheme outcomes throughout the time interval. Discuss the computational cost of the schemes in terms of time. The investigation emphasizes the precision and potency of the suggested schemes as compared to the other traditional schemes.

Keywords

• covid-19
• galerkin-scheme
• runge-kutta scheme
• prcc
• lyapunov function
• numerical comparison