Modeling the kinetics of the neutralizing antibody response against SARS-CoV-2 variants after several administrations of Bnt162b2 vaccine
Quentin Clairon (1,2,3), Mélanie Prague (1,2,3), Delphine Planas (3,4), Timothée Bruel (3,4), Laurent Hocqueloux (5), Thierry Prazuck (5), Olivier Schwartz (3,4), Rodolphe Thiébaut (1,2,3), Jérémie Guedj (6)
(1) Université de Bordeaux, Inria Bordeaux Sud-Ouest, (2) Inserm, Bordeaux Population Health Research Center, SISTM Team, UMR1219, F-33000 Bordeaux, France, (3) Vaccine Research Institute, F-94000 Créteil, France, (4) Virus and Immunity Unit, Institut Pasteur, Université de Paris Cité, CNRS UMR3569, Paris, France, (5) Service des Maladies Infectieuses et Tropicales, Centre Hospitalier Universitaire, Orléans, France, (6) Université Paris Cité, IAME, Inserm, F-75018 Paris, France
Objectives: Developed vaccines against SARS-CoV-2 have been a turning point against the ongoing Covid-19 pandemic by dramatically reducing the number of sever cases as well as infection and transmission rates. Still, the initial vaccine efficacy against the historical viral strain has been jeopardized by two phenomena. Firstly, the waning immunity due to antibody decrease over time. Secondly, the apparition of various Variants of Concern (VoCs) that partially escape the neutralizing action of vaccine induced antibodies. As a countermeasure, additional injections were used to re-establish significant antibody population and ensure a long-term neutralizing activity. To infer if this multi-dose strategy fulfils such task, it is therefore essential to measure not only antibody concentration over time, but also how this translates in terms of neutralization capacity. For that purpose, we relied on data from a cohort of Bnt162b2 vaccine recipients, in which two types of measurements were available 1) the total number of anti-spike binding IgGs (measured in BAU/ml) 2) the neutralization titers against each VoC (measured in ED50, the higher the better). We constructed a model for both quantities simultaneously, allowing us to quantify the gain brought by each new injection in terms of quantity and “quality” of the antibody response. Finally, we use the model to predict the long-term evolution of neutralizing activity.
Methods: We relied on a prospective cohort (presented in ) of N=26 SARS-CoV-2 naive patients who received up to three vaccine doses with an average follow-up of 11 visits after the first injection with a median follow-up time of 362 days. The ED50 were available for D614G, Beta, Delta and Omicron subvariants BA.1, BA.2 and BA.5. Then, we construct a model composed of:
- an ordinary differential equation (ODE) to predict antibody concentration evolution from the first to the last injection 
- a functional part quantifying the neutralizing activity of antibodies against VoCs.
The analysis of the vaccine induced immune response is then turned into a parameter estimation problem solved with Monolix  in a nonlinear mixed-effect framework.
Results: Because our model distinctly accounts for the effect of VoC, antibody concentration variation and injection number on the induced neutralization, we identify two mechanisms that led to a marked increase in humoral response over the successive vaccination doses. In addition to the increase in IgG levels after each dose, we identified that antibody affinity was significantly increased against all VoCs after each new injection. Our model also enlightens the dramatic differences in neutralization gain among the VoCs. In particular, accounting for a VoC specific neutralization gain after the third injection higher than the one given by second dose has significantly improved model quality (in terms of AIC). Consequently, the model projects that the mean duration of detectable neutralizing capacity against non-Omicron VoC after the third injection is between 348 days (Beta variant, 95% Prediction Intervals PI [307; 389]) and 587 days (Alpha variant, 95% PI [537; 636]). The mean duration of detectable neutralizing capacity against Omicron variants varies between 173 days (BA.5 variant, 95% PI [142; 200]) and 256 days (BA.1 variant, 95% PI [227; 286]).
Conclusions: This work proposes the first mathematical model to analyze the joint kinetics of antibody concentration and neutralization. It precisely quantifies the effect of multiple injections on the measured neutralization level and the dramatic differences between VOCs. This enlightens the need to measure the actual antibody neutralizing activity, in addition to their concentration, to infer the longevity of the vaccine induced humoral protection for a given viral strain. Despite this model relies on several simplifying assumptions, for examples on the B-cells dynamics sustaining antibody production and the linear relationship between antibody concentration and neutralization, it provides predictions on the long-term evolution of neutralizing activity in a vaccinated population. This can help to design better suited injection schedule when and if a correlate of protection expressed in terms of neutralizing activity is found.
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