Method for quantitative assessment of protective immunity against SARS-CoV-2, its duration and antibody dynamics

Abstract

The level and duration of protective immunity are often analyzed qualitatively or semi-quantitatively. The same strategy is applied to the analysis of antibody dynamics. At some point in time t after exposure or immunization, the presence of immunity against the infection is inferred from the level of specific antibodies by comparing it to a reference value. This approach does not account for the stochastic nature of human disease after exposure to a pathogen. At the same time, it is not fully clear what antibody level should be considered protective. The aim of this study was to develop a mathematical model for quantitative determination of protective immunity against SARS-CoV-2 and its duration. We demonstrate that the problem of describing protective immunity in quantitative terms can be broken down into 2 interrelated problems: describing the quantitative characteristics of a pathogen’s virulence (in our case, the pathogen is SARS-CoV-2) and describing the dynamics of antibody titers in a biological organism. Below, we provide solutions for these problems and identify parameters of the model which describes such dynamics. Using the proposed model, we offer a theoretical solution to the problem of protective immunity and its duration. We also note that in order to quantitatively determine the studied parameters in a homogenous population group, it is necessary to know 5 parameters of the bivariate probability density function for correlated continuous random variables: the infective dose of the pathogen and the antibody titer at which the disease develops and which are still unknown.