Vaccination, Immunity and Breakthrough: Quantitative Effects in Individual Immune Responses Illustrated by a Simple Kinetic Model

Abstract

The personal risks of infection, as well as the conditions for achieving herd immunity, are strongly dependent on an individual’s response to the infective agents on the one hand, and the individual’s reactions to vaccination on the other hand. The main goal of this work is to illustrate the importance of quantitative individual effects for disease risk in a simple way. The applied model was able to illustrate the quantitative effects, in the cases of different individual reactions, after exposition to viruses or bacteria and vaccines. The model was based on simple kinetic equations for stimulation of antibody production using different concentrations of the infective agent, vaccine and antibodies. It gave a qualitative explanation for the individual differences in breakthrough risks and different requirements concerning a second, third or further vaccinations, reconsidering different efficiencies of the stimulation of an immune reaction.