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

=== Assistant: The short answer is susceptible replenishment plus nonlinear transmission. ===
The short answer is susceptible replenishment plus nonlinear transmission. The longer answer has a few interacting pieces that make measles outbreaks look “cyclical” rather than smooth.

==== 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.

==== 2. Vaccination turns steady endemic disease into bursts ====

Before widespread vaccination, measles showed regular multi-year cycles (often 2–5 years). High vaccination coverage fundamentally changes the regime:
* Transmission is mostly suppressed.
* But suppression is fragile.
* Small drops in coverage or clustering of unvaccinated individuals allow large, punctuated outbreaks.

So paradoxically, better control leads to spikier dynamics:
* Long quiet periods
* Followed by sudden large outbreaks once herd immunity locally fails.

This is visible in your chart: long low baselines punctuated by sharp peaks.

==== 3. Spatial and social clustering matters more than averages ====

National vaccination rates can look fine while outbreaks explode locally.

Key point: herd immunity is not linear in space or networks.
* Schools, religious communities, or social groups with low uptake create dense susceptible clusters.
* Measles spreads explosively within these clusters, then spills outward.
* After the cluster is “exhausted,” transmission again collapses.

This produces irregular cycles rather than clockwork periodicity.

==== 4. Stochastic sparks + global connectivity ====

Measles is often reintroduced via:
* international travel,
* importation from countries with ongoing transmission.

Whether an importation fizzles or ignites an outbreak depends on whether the susceptible pool is just above or below the threshold at that moment.

This creates:
* apparent randomness in timing,
* but systematic dependence on accumulated susceptibility.

So the system looks noisy, but it’s not arbitrary.

==== 5. Why recent peaks look larger ====

Two reinforcing trends:
* Slow erosion of vaccination coverage (hesitancy, access issues, pandemic disruptions).
* Longer inter-outbreak intervals, allowing larger susceptible build-ups.

Longer quiet → bigger crash when it finally comes.

This is not a contradiction of vaccine effectiveness; it’s exactly what highly effective but imperfect coverage predicts.

==== Bottom line ====

The cycles are not seasonal quirks or reporting artifacts. They arise because:

: measles transmission is threshold-driven,
: immunity is gradually replenished,
: and outbreaks rapidly reset the system.

If you want, we can:
* formalize this with a simple SIR or SIRS model,
* show how clustering changes cycle amplitude,
* or discuss how this differs from diseases with lower R₀ (like influenza).