Effect of partially and fully vaccinated individuals in some regions of India: A mathematical study on COVID-19 outbreak

Abstract

In this paper, we investigate the effect of partially vaccinated and fully vaccinated individuals in preventing the transmit of COVID-19, especially in the regions of Tamil Nadu, Maharashtra, West Bengal and Delhi. Here we construct an SEIR model and analyse the behaviour. We obtained R₀ by using next generation matrix approach. Also, our system shows two types of equilibria, namely disease free and endemic equilibrium. For both disease free and endemic equilibrium, local and global stability is obtained here. Our disease-free equilibrium is locally asymptotically stable whenever R₀ is less than one, whereas the endemic equilibrium is locally asymptotically stable whenever R₀ is greater than one. Furthermore, the global stability of disease-free equilibrium has been proven by using Lyapunov function and the global stability of endemic equilibrium has been obtained by using Poincare Bendixson technique. Also, we enhance our analytic results by numerical simulation. At the end we have attempted to fit our proposed model with the real-world data.