Dynamic Mathematical Model Analysis of the COVID-19 Epidemic with a Focus on Effective Numerical Schemes

Abstract

The new respiratory illness known as COVID-19 can cause pneumonia and, in severe cases, a highly sensitive respiratory condition. The duration of time the virus stays on surfaces varies based on factors such as sunlight, temperature, and the type of surface. In this research paper, we examine a mathematical model of COVID-19 which considers both symptomatic and asymptomatic individuals, and we analyze its behavior. The largest number in the reproductive model is an indisputable signal of the extent of an epidemic's severity. The article demonstrates that the NSFD scheme outperforms the Euler and RK4 numerical schemes. We have developed a new way of modeling called the nonstandard finite difference (NSFD) scheme. It maintains the essential qualities of the continuous model, such as being positive and bounded. To assess the stability of the NSFD model, we use the Schur-Cohn criterion locally for disease-free and endemic equilibria. We then use the Lyapunov function theory for global stability analysis. To enhance our comprehension of state variables and to reinforce our theoretical conclusions, we conducted simulations with different parameter values. The results of these simulations demonstrate that our method behaves in a manner that is closely aligned with the continuous model.