2109.01457
Optimal Control applied to SIRD model of COVID 19
Amira Bouhali, Walid Ben Aribi, Slimane Ben Miled, Amira Kebir
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper rewrites the Bolza cost J(u1,u2)=A1 D(tf)+∫ A2 u2^2 dt into a pure Lagrange form using Ḋ=(1−α)(u2+δ)I (its Eq. (8)), then applies PMP with Hamiltonian H=<λ, Ẋ>+A1(1−α)(u2+δ)I+A2u2^2, derives the adjoint ODEs with terminal condition λ(tf)=0, reduces to λ3≡λ4≡0, and obtains u1 as bang–bang and u2 as the projection of the unconstrained minimizer, exactly as in Theorem 3.2 and the explicit control laws stated thereafter . The candidate solution mirrors these steps (including the Bolza–Lagrange equivalence and the same adjoint system and feedback laws), so the two are essentially the same derivation.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper correctly applies Pontryagin’s Minimum Principle to a SIRD model to derive the optimality system and control laws. The Hamiltonian, adjoint dynamics, transversality, and the characterization of u1 as bang–bang and u2 via projection are consistent and well-aligned with standard theory. Minor revisions would improve presentation: clarify the Bolza–Lagrange equivalence and terminal conditions, fix a small typographical slip in one Hamiltonian line, and explicitly note edge cases in the minimization with respect to u1.