Mathematical Model for Coronavirus Disease 2019 (COVID‐19) Containing Isolation Class

TLDR

COVID‑19 remains a global pandemic, and mathematical models are used to track suspected, recovered, deceased, and tested cases while uncertainty persists about lasting immunity after infection. This study aims to improve predictions of COVID‑19 spread by incorporating an isolation class into a mathematical model. The authors formulate a compartmental model with an isolation class, prove its positivity and stability, and solve it numerically using a non‑standard finite difference scheme and Runge‑Kutta 4th‑order method. Simulations indicate that human‑to‑human contact drives outbreaks, and isolating infected individuals can substantially reduce future spread.

Abstract

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID‐19 infection means you gain long‐lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID‐19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge‐Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID‐19. Therefore, isolation of the infected human overall can reduce the risk of future COVID‐19 spread.