Prime-Boost Vaccination: Stochastic Clonal Kinetics (2D)

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.

Patient 1 — Clonal State

Antibody titer

0.00 AU

Active plasma clones B

Memory clones M

0 / 10

Founder clones ever activated

Peak titer (prime)

—

Peak titer (boost)

—

Peak-titer range across all 6 patients

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How it works

The flagship 3D version of this simulator integrates a smooth deterministic ODE — the same handful of antigen, plasma-cell, antibody and memory equations every "patient" follows identically. Real immune responses do not: only a small, random number of naive B-cell clones actually recognize a given vaccine epitope, and each one is individually born, divides or dies. This 2D version replaces the ODE for B (plasma clones) and M (memory clones) with an exact stochastic jump process — the same class of algorithm (Gillespie's Stochastic Simulation Algorithm) used in real computational systems biology:

reactions (each an individual, random, whole-clone event):
  activation:  ∅ → B     rate = β·A·(1 + k·M/Mmax)
  exit:        B → ∅     rate = δ_B·B
  memory form: ∅ → M     rate = γ·B·(1 − M/Mmax)
  memory loss: M → ∅     rate = δ_M·M

waiting time to the next event is drawn from the exact
exponential/thinning distribution set by these rates — never
a fixed time-step — so the clone counts B and M are always
whole numbers, exactly as real cell populations are.

Antigen A and antibody titer Ab stay continuous (there really are billions of antibody molecules), but are advanced with the closed-form exact solution of their linear decay/production equations between clone events, not a numerical integrator. Run many independent patients with identical settings and their mean converges to the flagship's deterministic curve — a real result called the thermodynamic/system-size limit — but any single patient can scatter well above or below it, and a patient can even go extinct (zero clones activated) after a weak prime dose purely from bad luck. That is a real, documented phenomenon: some vaccinees are "low responders" or "non-responders" for reasons that have nothing to do with the vaccine's average efficacy.

6 stochastic patients toggle — runs six independent clone-level simulations from the same doses simultaneously; the graph shows all six titer curves plus how far Patient 1 (bold) sits from the pack.
Founder clones ever activated — a running count of every individual activation event Patient 1 has had; compare it across repeated resets at the same dose to see the real variability the ODE model hides.
Adjuvant potency — multiplies β, the per-clone activation rate, exactly as in the flagship model.

Day 0.0

Plasma clone (Patient 1) Memory clone (Patient 1) Free antigen