Category: Epidemiology

Summary: Finding when broader CRISPR spacer cross-reactivity and lysogenic refuge turn phage escape from a single lytic lineage into a distributed lytic-lysogenic cloud.

CRISPR immunity can suppress phage, but that pressure also drives escape, and temperate phages can survive partly through lysogeny. This experiment asks when those ingredients combine to change the structure of the leading growth mode: instead of concentrating on one lytic escape lineage, the system may spread across a broader cloud that includes both lytic and lysogenic components.

The model builds dense symmetric operators over immune, escape, and lysogeny profiles, then increases spacer cross-reactivity while measuring how the dominant eigenvector redistributes its mass. Iterative deepening and eigensolve-based bisection locate the crossover point across larger operator sizes, using participation and component-weight statistics to distinguish a narrow escape mode from a broad lytic-lysogenic cloud.

That focus makes the experiment a spectral transition study of host-phage immune structure rather than a simple infection-count simulation. The value is in identifying the threshold where broader immune memory and lysogenic refuge qualitatively reorganize the escape landscape.

Method: Dense symmetric eigensolves with iterative deepening and bisection on spacer cross-reactivity kappa across N=64 to 2048 operators.

What is measured: Critical cross-reactivity threshold, cloud score, immune mass, escape mass, lysogen mass, participation ratio, peak mass, leading eigenvalue, and bracket width.