§17 · application: vaccine kinetics
The prime-boost interval is interior-optimal; saRNA reaches the protected basin more reliably
The boost benefit peaks at an interior optimum (best interval 3 rounds, benefit 0.0311): boost too early and the response has not matured, too late and protection has decayed at the measured escape rate (0.0244). A longer same-amplitude saRNA window crosses the protected basin more reliably than mRNA (0.5317 vs 0.5072); post-flip durability is the identical barrier. [V].
On the memory master PAX5 (γ = 1.4892) with a measured escape rate of 0.0244, the boost benefit is an inverted-U peaking at 3 rounds (0.0311) with both arms worse. Near the spinodal (0.6995) at equal amplitude 0.6645, a 1200-step saRNA window crosses 0.5317 of the time versus 0.5072 for a 400-step mRNA pulse.
The prime–boost interval has an interior optimum
The boost is swept in germinal-centre rounds — the IM1 maturation loop reused unchanged — with the primed pool decaying at the measured escape rate (0.0244). Boost too early and the response has not matured; boost too late and protection has already decayed. The benefit is a genuine inverted-U with an interior peak at 3 rounds (0.0311); both arms are worse, and the long arm keeps fading out to the end of the sweep.
| interval (rounds) | maturation gain | primed survival | boost benefit |
|---|---|---|---|
| 1 | 0.0246 | 0.9759 | 0.0240 |
| 2 | 0.0322 | 0.9524 | 0.0307 |
| 3 | 0.0335 | 0.9295 | 0.0311 |
| 4 | 0.0339 | 0.9071 | 0.0307 |
| 5 | 0.0328 | 0.8853 | 0.0291 |
| 6 | 0.0335 | 0.8640 | 0.0290 |
The optimum tracks the maturation endpoint against the decay; mapping substrate rounds to calendar days needs an in-vivo rate that is not measured here, so the absolute interval is [O].
saRNA reaches the protected basin more reliably than mRNA
Near the spinodal (0.6995) at the same amplitude (0.6645, noise D = 0.30), a longer saRNA drive window (1200 steps) crosses into the protected basin more often than a shorter mRNA pulse (400 steps): 0.5317 versus 0.5072. The advantage is in reaching: once flipped, durability is the identical barrier (the same γ), so saRNA holds no longer than mRNA once both have crossed. The reliability ordering is read; the absolute titre and amplification factor are [O].