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The Value of Modeling and Simulation in Vaccine Development

In an earlier blog, I outlined a project to develop a Modeling & Simulation (M&S) timing model – as an alternate approach to dedicated clinical studies – to determine the best time to vaccinate pregnant women. This model could then be further employed to predict infant antibody (Ab) levels at birth and ultimately be used as a valuable quantitative approach to vaccine development.


Fit to Maternal Antibody Data

To assess how well our model will fit with the existing trial study data, the timing model simulations were compared to the maternal vaccination data obtained from studies conducted by the Maternal Immunization Working Group in the Centers for Disease Control (CDC) in South Africa, Mali, and Nepal. The model was trained using the South Africa and Mali trial datasets, and the Nepal data was used as an external validation step.

The results of the simulation demonstrated that the model adequately captures the baseline, the rise, and the fall of maternal titer levels. The model fit data was represented in a box plot based on number of visits, plotting Time after Vaccination in weeks (x-axis) versus Antibody Titer (y-axis). Determination of antibody titers was a complicated process – the assay studies were conducted in each study center lab versus a single central lab facility. The antibodies are assessed through an initial dilution of the sample – which is different across trials – and then serially diluted until the sample does not block a signal in an in vitro assay. The reported dilution values represent digital or ordered categorical data.

Box Plot to Demonstrate Model Fit to Maternal Influenza Antibody data


The median of the data is shown by the horizontal lines in each of the boxes and the 5th and 95th percentile of the data appears as the extent of the box. The model fits are shown as the median of prediction (the solid blue line) and variation/variability (blue envelope). The model was shown to fit to the study data as ideally the median and the prediction should line up with the data median and the variation/variability in the envelope coincide with the edges of the box plots as demonstrated in the plot.

We also gain knowledge from these simulations – we know that it takes 20 days to recruit plasma cells to start producing antibodies. With simulations, we find that over a one year period, 85% of the titer is produced by long-lived plasma cell population and short-lived plasma cells have a three day half-life. So, a large amount of antibodies are produced immediately which, over a time span of weeks, might be a very important cell population.

We are also conducting a covariate search to help understand the factors contributing to the heterogeneity seen in the data.


Time to Maximal Influenza Antibody Production

The model was also used to perform simulations to predict the time course of antibody production after vaccination: a sharp rise occurs approximately 20 days after vaccination, peaks at around 8 weeks, then slowly declines after the peak due to antibody turnover and plasma cell population turnover.

Another simulation was performed to compare to the Nepal data set, which contained a much sparser sampling schedule and less subject data versus the South Africa and Mali datasets. In this simulation, we were able predict study results by looking at the medians 13 weeks post-vaccination thus establishing an important validation step for this project.


Using the Timing Model to Simulate Optimal Timing of Other Vaccines

To see how our model simulation results on predicting maternal influenza antibody compared to existing studies for other vaccines, we compared the influenza simulation results to Tdap (Tetanus, Diphtheria, Pertussis) studies. The Advisor Committee on Immunization Practices (ACIP) recommends that the Tdap vaccine be administered to pregnant women between 27 – 36 weeks of gestation. An independent Tdap prospective study conducted by Eberhardt and colleagues on 335 pregnant women immunized in the second or third trimester concluded that contrary to the ACIP recommendation, the early second trimester produced a higher infant antibody titer.1 Our simulation, on predicted maternal influenza antibody titers, closely matched the infant Tdap titer optimum reported by Eberhardt showing alignment of the influenza vaccine in the Tdap titer kinetics.

This is an exciting observation, which raises an intriguing question. These two vaccines utilize the same humoral immunity system to produce these antibodies. Since we obtained similar kinetic patterns with two different vaccines, are these kinetics characteristic of many vaccines? These findings suggest that more precise recommendations on vaccine administration are possible, i.e. 6 to 8 weeks prior to delivery.


Predicting Infant Influenza Antibodies at Birth

Our next step is to establish the efficacy of this model was to determine the consistency of the infant: maternal antibody ratio at birth.

Predicted versus Observed Infant Influenza Antibodies at Birth


Our findings indicated that the infant antibody titer highly correlates to the maternal ratio at birth. Most importantly, a comparison of predicted versus observed infant birth titers demonstrated relatively good alignment indicating that the maternal antibody level can be used to predict the infant antibody level at delivery.

Other aspects of the model we examined were to predict infant antibody levels with respect to time. For example, body weight, gestational age, and postnatal age are known factors that impact antibody clearance in children.


Looking to the Future – Linking Infant Influenza Antibody Titer Level to Protection

Our future work will focus on using the model to determine how infant antibody levels correspond to protection against influenza. We continue to collaborate with the Maternal Influenza Immunization Data Analysis Working Group to uncover the relationship between titer level and protection. Once this work is completed, we will have established a quantitative modeling approach to determine the sequence of events – from vaccination in the mother to quantitative assessment of protection in infants. It is feasible to run simulations to derive permutations of all possible times for vaccinating mothers, obtain protection curves for the infants, and ultimately pinpoint the response curve of protection relative to the mother’s vaccination time.



  1. Eberhardt,S., Blanchard-Rohner,G., Lemaître, B., et al. (2016).  Maternal Immunization Earlier in Pregnancy Maximizes Antibody Transfer and Expected Infant Seropositivity Against Pertussis. Clin. Infect. Dis., 62(7), 829-836.


To learn more on how this timing model can be used to optimize maternal antibody levels and predict infant antibodies at birth, please watch this webinar I conducted on this project.

About the author

Michael Dodds
By: Michael Dodds
Specializing in pharmacometrics application to complex biotechnology products since 2005, Mike’s research focuses on the application of mathematical models of biology, (patho)-physiology, pharmacology and disease that quantify beneficial and undesirable interactions between drugs and patients to predict outcomes. He has held roles at ZymoGenetics and Amgen.

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