Optimal Control of an Impulsive VS-EIAR Epidemic Model with Application to COVID-19

MAMADOU ABDOUL DIOP, MOHAMMED ELGHANDOURI, KHALIL EZZINBI

incompletemedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper correctly formulates the VS–EIAR control problem, derives the Hamiltonian, adjoint system, and projection formulas, and asserts existence of an optimal triple, but it (i) states uniqueness from strict convexity of J without adequate justification for this nonlinear state dynamics setting and (ii) omits the free–terminal–time transversality condition H(τ*) + M'(τ*) = 0. The model’s solution supplies the missing free–time transversality and gives a sound existence argument, but its uniqueness argument relies on BVP uniqueness that is not warranted in general. Thus, both are largely correct on PMP structure and existence, but both are incomplete on uniqueness.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript presents a solid application of PMP to a vaccination-augmented SEIAR model, with clear derivations of adjoint dynamics and explicit control laws. The results are relevant and well-motivated. However, the uniqueness claim requires qualification because strict convexity of the running cost does not ensure uniqueness for nonlinear state dynamics, and the free-terminal-time transversality condition is not stated. These issues can be addressed with modest revisions.