Table 1.
Parameter values employed in the model. Parameter values are similar to our previous model (25).
| Model parameter | Symbol | Units | Value(s) |
|---|---|---|---|
| Rate constant for antibody-antigen binding | k | s -1 day -1 | 0.0005 |
| Decay rate of free and bound antigen | dAg | day -1 | 1 |
| Decay rate of antibody | dAb | day -1 | 0.1 |
| Maximum proliferation rate of B cells | λ | day -1 | 1 |
| Antigen amount that stimulates half-maximal proliferation of B cells | ϕ | s | 100 |
| Antibody production rate (rescaled so that Antibody=B cell at steady state) | p | day -1 | 0.1 |
| Decay rate of B cells | dB | day -1 | ln(2)/47 |
| Fraction stimulation of B cells in secondary responses by non-homotypic antigen | f | – | 0.075 |
| Antigen dose for vaccinations #1 and #2 | – | s | 105 |
| Antigen dose for vaccinations #3, #4 and #5 | – | s | 0.5 × 105 |
| Time of vaccinations #1 – #5 | – | day | (0, 4, 41, 75, 100) * 7 |
| Ratio of conserved to unique antigen epitopes | m : n | – | 1:5 |
dB was chosen based on an analysis of waning vaccine immunity following two doses of the mRNA vaccine in naïve individuals (70). f is a free parameter expected to be significantly less than 1, and we chose 0.075 to qualitatively match the experimental observations of Gagne et al ( Figure 3 ). We note that s is scaled concentration units, and the initial concentration of B cells is rescaled to 1. For comparing simulations with the influenza data ( Figure 5 ), we set the antibody detection threshold as 5 × 103 AU to account for the background or pre-vaccine antibody titer in experiments. The time of vaccinations #1-#3 was taken from the study design of Gagne et al. (28) For immunizations #4 and #5, we allowed an interval of a few months as might be seen for vaccine boosters. In all our simulations, we have matched the times of immunization to that in the relevant study (mice experiments, primate experiments, or human clinical studies).