Mathematical modelling of the waning of anti-RBD IgG SARS-CoV-2 antibody titers after a two-dose BNT162b2 mRNA vaccination

BACKGROUND: After exposure to SARS-CoV-2 and/or vaccination there is an increase in serum antibody titers followed by a non-linear waning. Our aim was to find out if this waning of antibody titers would fit to a mathematical model. METHODS: We analyzed anti-RBD (receptor binding domain) IgG antibody titers and the breakthrough infections over a ten-month period following the second dose of the mRNA BNT162b2 (Pfizer-BioNtech.) vaccine, in a cohort of 54 health-care workers (HCWs) who were either never infected with SARS-CoV-2 (naïve, nHCW group, n=27) or previously infected with the virus (experienced, eHCW group, n=27). Two mathematical models, exponential and power law, were used to quantify antibody waning kinetics, and we compared the relative quality of the goodness of fit to the data between both models was compared using the Akaik Information Criterion. RESULTS: We found that the waning slopes were significantly more pronounced for the naïve when compared to the experienced HCWs in exponential (p-value: 1.801E-9) and power law (p-value: 9.399E-13) models. The waning of anti-RBD IgG antibody levels fitted significantly to both exponential (average-R2: 0.957 for nHCW and 0.954 for eHCW) and power law (average-R2: 0.991 for nHCW and 0.988 for eHCW) models, with a better fit to the power law model. In the nHCW group, titers would descend below an arbitrary 1000-units threshold at a median of 210.6 days (IQ range: 74.2). For the eHCW group, the same risk threshold would be reached at 440.0 days (IQ range: 135.2) post-vaccination. CONCLUSION: Two parsimonious models can explain the anti-RBD IgG antibody titer waning after vaccination. Regardless of the model used, eHCWs have lower waning slopes and longer persistence of antibody titers than nHCWs. Consequently, personalized vaccination booster schedules should be implemented according to the individual persistence of antibody levels.