Category: Epidemiology

Summary: Finding the intergenerational-contact threshold where an epidemic mode leaves an under-immunized adolescent band and shifts toward caregiver-dominated spread.

Age-structured epidemics are shaped both by contact patterns and by uneven immunity across age groups. This experiment asks when stronger bridge contact between generations causes the dominant outbreak mode to stop concentrating in a narrow adolescent immunity gap and instead relocalize onto caregiver-heavy age bands.

The script builds dense age-structured operators with noisy contact structure and a localized immunity deficit, then uses iterative deepening and eigensolves to bisect the bridge-contact threshold across larger systems. The analysis focuses on where the leading epidemic mode sits, not only on whether total transmission grows.

That emphasis makes the result useful as a structural transition marker. It targets the point where intergenerational mixing changes who effectively carries the epidemic, which can matter for control strategies even before aggregate growth shifts dramatically.

Method: Dense symmetric eigensolves with iterative deepening and bisection on intergenerational bridge strength eta across N=64 to 2048.

What is measured: Critical bridge-contact threshold, adolescent versus caregiver dominance of the leading mode, localization profile, leading eigenvalue, and bracket width.