Editing Openai/6946e1f5-6b14-800c-a0ce-b10e5c3d84dd (section)

==== 1. Depletion–replenishment dynamics (the core mechanism) ====

Measles is extremely contagious (R₀ ≈ 12–18). When an outbreak happens, it rapidly burns through the pool of susceptible people:
* unvaccinated children,
* people with waning immunity,
* recent immigrants or cohorts that missed vaccination.

After a big outbreak, there simply aren’t enough susceptibles left to sustain transmission, so cases collapse.

Over time, susceptibles re-accumulate via:
* births,
* missed or delayed vaccinations,
* waning immunity (minor but nonzero),
* migration from lower-coverage areas.

Once the susceptible fraction crosses a threshold, the system becomes unstable again → another outbreak.

This is classic SIR dynamics and produces oscillations even with perfectly constant behavior.