An Improved Mathematical Model of Sepsis: Modeling, Bifurcation Analysis, and Optimal Control (Study for Complex Nonlinear Infectious Disease System)

Yuyang Chen, Kaiming Bi, Chih-Hang J. Wu, David Ben-Arieh, Ashesh Sinha

incompletemedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper formulates the anti–TNF-α optimal control by inserting the measurable control u_T only into the TNF-α ODE (Eq. (41)) and minimizing the biomarker ratio ∫ T/CA (Eq. (42)), then solves it numerically with an RNN-BO algorithm, but it provides no mathematical analysis of well-posedness, existence of an optimal control, or PMP conditions. The candidate solution correctly supplies those missing pieces (well-posedness/positivity, uniform a priori bounds, Filippov–Cesari existence, and PMP with a bang–bang characterization), consistent with the model equations and objective stated in the paper.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work formulates a comprehensive sepsis model and a clinically motivated optimal control objective, and it demonstrates an efficient heuristic (RNN-BO) numerically. However, the optimal control section lacks foundational analysis: it does not establish existence and uniqueness of trajectories, existence of an optimal control, or PMP necessary conditions. Given the complexity of the ODE system, adding minimal analysis (well-posedness on a finite horizon, existence via a standard theorem, and PMP) is essential. Clarifying duplicated equations and assumptions ensuring the ratio T/CA is well-defined would significantly improve rigor.