<p>COVID-19, a perilous disease triggered by the SARS-CoV-2 virus, exhibits an unusually high spread rate through both direct and indirect physical contact. There are many ways to inspect the possibility of COVID-19 which may include but not limited to shortness of breath, fatigue, strict headaches, tastelessness, continuous chest pain, diarrhea and vomiting. In the present paper, the COVID-19 deterministic mathematical model with cost effectiveness strategies is considered and examined. The threshold quantity, assisting in establishing the existence and stability characteristics of equilibria, is computed by employing the next-generation matrix. The main objective of the present work is to use conditionally stable Euler and Runge–Kutta of order 4 (RK-4) schemes with the collaboration of unconditionally stable non-standard finite difference (NSFD) scheme to show the changing behavior of consistent SEIHR epidemic model. The Euler and RK-4 schemes are unable to precisely focus on the important aspects of the continuous model, resulting in numerical solutions that are not entirely analogous to the original model. However, the NSFD scheme provides a straightforward approach that demonstrates how discrete and continuous models behave appropriately and yield mathematically precise results. The NSFD system is a useful tool for tracking the spread of COVID-19 disease. For the NSFD scheme, different criteria and theories are employed to discuss the local and global stability of disease-free and endemic equilibria. Numerical simulations are provided to verify the theoretical findings and validate the dynamical aspects of the aforementioned schemes.</p>