Mathematical modeling of the vaccination influence on the COVID-19 epidemic propagation

Abstract

The mathematical model based on a system of ordinary differential equations is proposed to describe the effect of the vaccination rate on the spread of the COVID-19 epidemic. The results of numerical modeling are presented for the case when vaccination begins after the beginning of the epidemic. A dimensionless vaccination parameter V was obtained, which allows one to characterize the effect of the vaccination rate on the reduction of the incidence of viral diseases with different virulence levels in a large closed population of people. Introducing this parameter allows the simulation results to be generalized to the populations of different size, different epidemic spread rate, different vaccination rate, and different vaccine efficiency. It has been shown that increasing the parameter V decreases the proportion of the sick population. It follows from our model that the vaccination influence on the spread of a respiratory viral disease such as COVID-19 decreases for a later initiation of vaccination. The simulation results should contribute to the development of optimal vaccination scenarios for the population.