Category: Epidemiology

Summary: Finding the commuter-leakage level where outbreak dynamics escape a poorly vaccinated school band despite protection from a highly vaccinated surrounding moat.

Vaccination campaigns are often uneven in space, with some places much better protected than others. This experiment asks when that patchwork protection stops containing an outbreak: specifically, when mobility allows the dominant epidemic pattern to leak out of an under-vaccinated school-centered region even though it is surrounded by a more highly vaccinated population.

The model builds a dense next-generation operator for a metapopulation with a school band, a vaccinated moat, and commuter coupling between locations. It then bisects the commuter-leakage parameter while increasing system size through iterative deepening, tracking the point where the leading epidemic mode is no longer localized behind the vaccinated barrier.

That matters because localized interventions can look effective in static analyses yet fail once realistic movement is included. The experiment turns that practical vulnerability into a finite-size threshold estimate rather than a qualitative caution.

Method: Dense non-symmetric eigensolve with iterative deepening and bisection on commuter leakage in a metapopulation next-generation operator.

What is measured: Critical commuter-leakage threshold, localization of the leading epidemic mode, system size reached, and threshold bracket width.