A New Mathematical Modeling of the COVID-19 Pandemic Including the Vaccination Campaign

Abstract

In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account the vaccine campaign among these studies. In this context, a mathematical model is developed to reveal the effects of vaccine treatment, which has been performed recently, on COVID-19 in this study. In the proposed model, as well as the vaccinated individuals, a five-dimensional compartment system including the susceptible, infected, exposed and recovered population is constructed. Moreover, besides the positivity, existence and uniqueness of the solution, biologically feasible region are provided. The basic reproduction number known as expected secondary infection which means that expected infection among the susceptible populations caused by this infection is evaluated. In the numerical simulations, the parameter values taken from the literature and estimated are used to perform the solutions of the proposed model. Fourth-order Runge-Kutta numerical scheme is applied to obtain the results.