Efficacy of pulse vaccination over constant vaccination in COVID-19: a dynamical analysis

Abstract

Today, the whole world is fighting against a dreadful pandemic COVID-19 with no substantial vaccination invented till now. Researchers, scientists are struggling hard to develop different vaccination strategies which can be of help to society. It’s a novel idea to pursue multiple strategies and platforms because we really don’t know what will work best. Keeping this in mind, in this paper we have developed a Susceptible-Infected-Removed(SIR) model of corona-virus with constant as well as pulse vaccination strategy in individuals to show that how vaccination strategy can also play an important role to control infection and block the virus production. The model is formulated for both constant vaccination and pulse vaccination by taking discrete and distributive delays and analysed the potency of vaccination along with delay. In the latter case, pulse Vaccination of the susceptible population takes place at periodic intervals. The system is studied for a special infection free case and is solved for a T-periodic solution. In both the systems, disease free equilibrium point is locally as well as globally attractive if the basic reproduction number(R₀ < 1) is less then 1 and the endemic point is stable provided R0 > 1. Further, we have compared the efficacy of constant and pulse vaccination plan and obtained an interesting result that pulse vaccination strategy has come up as a better strategy as it can lower the reproduction number comparatively and should followed frequently. In addition to it, if we extend the time period, it would be difficult to control the infection. Finally, all the theoretical results are verified with numerical simulation using MATLAB.