Optimal intervention strategies for minimizing total incidence during an epidemic

The paper proves that, under an L1 budget ||u||1 ≤ c1 and a maximal intervention level ||u||∞ ≤ c∞, the total incidence is minimized by a single constant-level lockdown of intensity c∞ and duration c1/c∞, with a unique optimal start time (Theorem 1) . Its proof executes a five-step reduction—(i) tail truncation via uniform integrability, (ii) quantization to bang–bang controls at level c∞, (iii) prolongation from the end reduces incidence, (iv) merging disjoint active intervals into a single block, and (v) uniqueness of the timing—exactly matching the model’s outline . The model’s solution is essentially the same scheme, with a slightly different monotonicity device (using H(t)=ln S+(β/γ)R so H′=βuI≥0) rather than the paper’s vulnerability function and special-function lemma in Appendix C . One minor defect in the model write-up is a sign slip: it claims the map S∞ ↦ ln S∞ + (β/γ)(N−S∞) is strictly decreasing, whereas on the relevant range S∞ ≤ γ/β it is strictly increasing; despite this, the model correctly concludes that larger terminal H yields larger S∞ and thus lower J. Overall, both arguments reach the same result with nearly identical reductions, and the paper’s proof is complete and correct.