Bifurcation analysis of a vaccination mathematical model with application to COVID-19 pandemic

Abstract

In this research, we propose a delayed vaccination model with the application for predicting the evolution of infectious cases related to COVID-19 disease. The main purpose of this paper is to show the existence of Hopf bifurcation that can explain the multiple waves that the world witnessed this recent times. Therefore, it can be used the length between the doses for the vaccine that considered for different vaccines and its effect on the evolution of the infectious cases. It has been shown that the investigated model can undergo Hopf bifurcation in presence of delay time lags to the vaccine against a COVID-19, and can lead to the persistence of the disease. The obtained mathematical findings are checked using graphical representations with proper interpretations on the manner of controlling the outbreak of COVID-19 disease.