Urban Epidemic Hazard Index for Chinese Cities: Why Did Small Cities Become Epidemic Hotspots?

The paper explicitly derives the vector form [I − α(W − diag(W))] h = (1−α) diag(U) 1 and the closed form h = (1−α)[I − α(W − diag(W))]^{-1} diag(U) 1 (its Eq. (9)), and notes the α=0 and α=1 boundary interpretations . The candidate solution reproduces the same derivation and adds a clean justification of invertibility/uniqueness for 0 ≤ α < 1 via strict diagonal dominance/Neumann series, and states the α=1 case correctly as an eigenvector condition without asserting existence. Thus both are correct with essentially the same proof; the model adds a minor, standard linear-algebra justification the paper omits.