Each dose triggers plasma cells to secrete antibody, and a fraction of the responding B cells differentiate into long-lived memory B cells. Three coupled quantities are integrated every frame:
dP/dt = −P/τP (plasma-cell secretion activity decays)
dA/dt = P − A/τA (titer A rises with secretion, decays with serum half-life)
dM/dt = −M/τM (memory pool decays very slowly)
On a dose of strength s at memory level M:
boost = 1 + k·M (anamnestic amplification)
P += s · boost
M += g · s / (1 + M/Mmax) (diminishing-returns recruitment)
- Primary dose — first exposure. No memory pool yet, so
boost ≈ 1: a slow, modest rise (~7–14 simulated days to peak, verified numerically) that decays back down over weeks.
- Booster dose — because memory B cells persist from the primary dose, the anamnestic (secondary) response fires with
boost > 1: production starts higher and the titer overshoots the primary peak while rising just as fast.
- Antibody titer — visualised as the swarm of small particles orbiting the germinal centre; particle count and glow track A(t) in real time. Drag the view to rotate it and see the orbit from a different angle — this only changes the camera, never the physics.
- Memory B-cell pool — the outer ring of gold nodes; it barely decays between doses (τM defaults to 260 days vs τA's 25), which is exactly why a booster produces a faster, larger response than the original dose.
- Serum half-life, memory persistence and boost strength are exposed directly as sliders here (fixed constants in most textbook treatments) — push τA down to see a spikier, faster-decaying titer, or push k up to see how much more a booster overshoots the primary peak.
- The dashed line on the scrolling titer chart marks the protective threshold used for the status readout above.
This is a simplified two-compartment pharmacokinetic model of humoral immunity — the same qualitative shape (slow primary rise, fast high secondary rise) is what real serology studies measure after prime-boost vaccination schedules (e.g. two-dose mRNA or hepatitis B series).