OPTIMAL SCREENING STRATEGIES IN THE CONTROL OF AN INFECTIOUS DISEASE: A CASE OF THE COVID-19 IN A POPULATION WITH AGE STRUCTURE

The paper sets up the same SEIRQ control problem (state system in (1) and (3)) and cost J(u)=∫Σ(Ii+Bi ui^2) dt as in the candidate solution, and then applies PMP to derive the Hamiltonian (6), the adjoint system with transversality (7)–(8), and the pointwise control characterization u*i = Proj[0,1]( Ii(λi^I−λi^Q)/(2Bi) ) given in (9)–(10) . The sign and index conventions in the adjoint equation for λi^I match the candidate’s derivation once the paper’s stated symmetry βij=βji is used . The paper cites standard existence and (small-time) uniqueness results rather than proving them in detail, while the candidate solution sketches the usual Filippov–Cesari existence argument and a contraction estimate for uniqueness; these are standard and consistent with the paper’s claims. Minor editorial gaps (e.g., not noting explicitly that λi^Q≡0 from λ′Q=τλQ with λQ(T)=0) do not affect correctness. Overall, both are correct and follow essentially the same PMP-based approach, with the candidate providing more explicit well-posedness/compactness details and a small-T uniqueness sketch.