• MATHEMATICAL MODELING OF THE SPREAD OF CORONA VIRUS IN PRESENCE OF VACCINATION

Abstract

We propose a COVID-19 model with vaccination. We have divided the total population into three subclasses: the susceptible population, vaccinated population and infective population. A separate class V(t) of cumulative density of corona virus in environmental reservoir is also taken into consider. Susceptibles are assumed to become COVID-19 infected via contacts with infectives and virus present in the reservoir. Model is analyzed using stability theory of differential equations. Both the infection-free and the endemic equilibria are found and their stability are investigated. Using Lyapunov functional approach, the sufficient conditions for global stability of the endemic equilibrium are obtained. It is shown that high rate of vaccination will help to reduce the infection in society. It is also found that the infective population can be decreased if susceptible do not come in direct contact with viral density deposited on surfaces/objects or airborne droplets accumulated in the environmental reservoir. Numerical simulations are also carried out to investigate the influence of key parameters on the spread of the disease, to support the analytical conclusion and illustrate possible behavioral scenario of the model.