Early detection of disease outbreaks and non-outbreaks using incidence data

The paper documents a simulation design with β(t)=β0+β1 t where β0,β1 are drawn from triangular distributions, and it labels 400-point pre-transition windows (T) versus randomly selected 400-point null windows (N) before testing five early warning indicators (SD, CV, AR1, skewness, kurtosis) via Mann–Whitney U; the findings are empirical (p≪0.001, near-perfect AUC on withheld synthetic tests) and do not claim a theorem that uniformly lower-bounds U away from 0.5 across all triangular priors or all parameterizations . The candidate solution correctly observes that such a universal δ>0 cannot hold without margin/separation assumptions and offers a plausible corrected theorem under explicit margins, but provides only proof sketches. Because the paper makes no corresponding uniform theoretical claim and the model provides only sketches rather than a full proof, both are incomplete from a rigorous theory standpoint.