Modeling antibody dynamics following herpes zoster indicates that higher varicella-zoster virus viremia generates more VZV-specific antibodies

Abstract

Introduction: Studying antibody dynamics following re-exposure to infection and/or vaccination is crucial for a better understanding of fundamental immunological processes, vaccine development, and health policy research.

Methods: We adopted a nonlinear mixed modeling approach based on ordinary differential equations (ODE) to characterize varicella-zoster virus specific antibody dynamics during and after clinical herpes zoster. Our ODEs models convert underlying immunological processes into mathematical formulations, allowing for testable data analysis. In order to cope with inter- and intra-individual variability, mixed models include population-averaged parameters (fixed effects) and individual-specific parameters (random effects). We explored the use of various ODE-based nonlinear mixed models to describe longitudinally collected markers of immunological response in 61 herpes zoster patients.

Results: Starting from a general formulation of such models, we study different plausible processes underlying observed antibody titer concentrations over time, including various individual-specific parameters. Among the converged models, the best fitting and most parsimonious model implies that once Varicella-zoster virus (VZV) reactivation is clinically apparent (i.e., Herpes-zoster (HZ) can be diagnosed), short-living and long-living antibody secreting cells (SASC and LASC, respectively) will not expand anymore. Additionally, we investigated the relationship between age and viral load on SASC using a covariate model to gain a deeper understanding of the population's characteristics.

Conclusion: The results of this study provide crucial and unique insights that can aid in improving our understanding of VZV antibody dynamics and in making more accurate projections regarding the potential impact of vaccines.

Keywords: antibody levels; herpes zoster; mathematical modeling; nonlinear mixed-effects models; ordinary differential equations; varicella zoster virus.

Figure 1

Individual-specific VZV IgG antibody titer concentration (expressed in mIU/ml) profiles by time (in days) since symptom onset in 61 herpes zoster patients. Data are shown per age group.

Figure 2

Schematic diagram depicting the different proliferation functions used to characterize antibody dynamics in the different models.

Figure 3

Observed antibody levels vs Model 6 predictions. The dots represent the observed data, while the y=x line represents the predicted values. The 95% predicted interval is also plotted, which shows the range within which we would expect 95% of the observations to fall. The plots are presented on both a linear scale (right) and a log-log scale (left). Overall, the figure suggests that the model predictions are in good agreement with the observed data, as the dots fall within the predicted interval for the majority of the data points.

Figure 4

Individual antibody response to VZV Reactivation in 12 participants using Model 6. Individual predictions using individual parameters and individual variables with respect to time on a continuous grid with observed VZV antibody data overlaid are displayed in this graphic. (more details about other participants are shown in Figure 9 ).

Figure 5

The Visual Predictive Check (VPC) comparing the results of the model-based simulations with observed data. The blue lines are empirical percentiles and summarize the observed data. The blue and pink areas are 95% prediction intervals and summarize predictions from the model 9. The observed percentiles are close to the predicted percentiles and remain within the corresponding prediction intervals.

Figure 6

The proliferation rate of SASC increases with the presence of a higher viral load. Correlation coefficient is 0.84 and p-value of 2.97×10^-15.