Mathematical and Numerical Analysis of COVID-19 Epidemic Model with Vaccination and Treatment

Abstract

Mathematical modeling is a broad field that greatly impacts and contributes to collaborative research investigations. The models Improve research on the fundamental the quantitative attitude and dynamics of diseases that are infectious that harm humans, including COVID-19, human immunodeficiency virus (HIV), and hepatitis B virus. This paper introduces a framework that supports the analysis of COVID-19 using an epidemic model that incorporates vaccination and treatment. The framework enables the examination of both non-pharmaceutical interventions and pharmaceutical interventions. The preservation of the basic reproduction number ensures the standardization of the stability of disease-free (DFE) and endemic equilibria. The local stability of the endemic and disease-free equilibria is proven using the Routh-Hurwitz criterion. The demonstration of disease-free and endemic equilibria convergence and divergence is demonstrated through the utilization of Standard and non-standard finite differences (SFD and NSFD, respectively) techniques. It might be argued that SFD schemes, specifically Runge-Kutta order four (RK-4) and Euler schemes, demonstrate convergence at smaller step sizes. However, the NSFD scheme is intended to enhance understanding of the dynamic behavior of the continuous model. Empirical evidence demonstrates that the NSFD technique converges, irrespective of the chosen step size. The latter refers to a powerful, effective, and dependable technique that provides a clear representation of the continuous model. Numerical simulations are employed to validate all the data, enhancing our understanding of the causes of the illness. The theoretical and quantitative results of its study can serve a valuable for mechanism tracking the transmission as to COVID-19.