Prime-Boost Vaccination: Antibody Titer Kinetics

Vaccination Schedule

Prime dose antigen 1.0×

Booster dose antigen 1.0×

Adjuvant potency 1.0×

Simulation speed 2.0 days/s

No dose given yet.

Immune State

Antibody titer

0 AU

Reciprocal dilution

<1:10

Plasma cells

0.00

Memory B pool

0.00

Peak titer (prime)

—

Peak titer (boost)

—

How it works

A compartmental ODE model tracks antigen A, activated plasma cells B, circulating antibody titer Ab and the long-lived memory B-cell pool M (all in arbitrary units, days as the time base):

dA/dt  = −δA·A                         (dose injects A → A+dose)
dB/dt  = β·A·(1 + k·M) − δB·B          (activation, scaled by adjuvant β)
dAb/dt = p·B − δAb·Ab                  (antibody secretion & clearance)
dM/dt  = γ·B·(1 − M/Mmax) − δM·M       (memory formation, saturating)

The key term is k·M in the activation equation: a naive immune system (M≈0) mounts a slow, modest primary response — titer rises over ~1–2 weeks and decays with roughly a 3-week antibody half-life (δAb). Once memory B cells have accumulated from the prime, a booster dose triggers the same equations but with M>0, so the activation term is amplified severalfold: the anamnestic (secondary) response rises faster, peaks far higher, and — because more antigen-experienced plasma cells differentiate — rebuilds an even larger memory pool. This is the real mechanistic reason booster shots work.

Prime / Booster dose sliders — scale the injected antigen A for each shot.
Adjuvant potency — multiplies β, the antigen-to-activation rate (models aluminum salts, lipid nanoparticles or other innate-immune-activating adjuvants that lower the antigen dose needed for a strong response).
Simulation speed — how many simulated days elapse per real second; the model is integrated with a fixed 0.02-day step regardless of display speed, so the dynamics are identical at any speed setting.

The 3D scene renders the plasma-cell colony as a pulsing central cluster (radius ∝ B) and circulating antibody molecules as orbiting particles (visible count ∝ Ab) — the graph plots log-scale titer vs. day so you can compare the primary and secondary response curves directly.

Day 0.0

Antibody molecules Plasma-cell colony Free antigen

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