A new fractional mathematical modelling of COVID-19 with the availability of vaccine

Abstract

The most dangerous disease of this decade novel coronavirus or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. The main aim of this paper is to justify the role of vaccine in this tough time of COVID-19. In this article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalise it in Atangana-Baleanu derivative sense. The motivation to use fractional derivatives is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor-Corrector algorithm to derive the solution and we also analyse its stability. We simulate number of graphs to see the role of vaccine on the population. For practical simulations, we use the parameter values which are based on real data of Spain. A clear role of vaccine at this crucial time can be realised by this study.