## Problem 212 — rank:245

**Title:** Transition to endemicity

**Added binding assumptions (LaTeX):**

```latex
Complete the susceptible equation by mass conservation and specify strictly positive initial infection for a persistence comparison. Stable periodic recurrence is defined relative to the forcing period or a declared subharmonic class. Uniform transient-time bounds can fail near bifurcations even in compact parameter sets; require separation from those boundaries or report an infinite compatible bound. Finite records distinguish regimes only through separated observable laws.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.