Discrete-Time System of an Intracellular Delayed HIV Model with CTL Immune Response

Sandra Vaz, Delfim F. M. Torres

correcthigh confidence

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

Audit review

The paper and the candidate arrive at the same trichotomy of global stability for the NSFD delayed HIV model and use broadly similar Lyapunov/G-telecoping machinery for the endemic regimes; the candidate’s disease-free regime uses a different, clean weighted-sum comparison that avoids a minor gap in the paper. Specifically, the paper’s Theorem 4 asserts ΔL_n ≤ 0 “for all n” using lim sup X_n = N1, whereas the boundedness lemma only ensures ultimate entry into X_n ≤ N1; this is readily fixed by claiming eventual (not uniform) monotonicity. The candidate’s arguments for R0 ≤ 1, R1 ≤ 1 < R0, and R1 > 1 are logically consistent and align with the paper’s results and discrete scheme. Citations: discrete scheme and delay set-up, equilibria and thresholds, and the three stability theorems with their Lyapunov functionals are explicitly in the paper (model (3) and Section 3.2).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The study robustly establishes the global dynamics of a discrete-time, delay-inclusive HIV model via NSFD and discrete Lyapunov methods. Its discrete scheme preserves key structural properties, and the stability proofs are in line with established techniques. One small clarification is needed in the disease-free case: the nonpositivity of a term is justified by ultimate boundedness, so the descent is eventual, not necessarily for all n. Addressing this strengthens the exposition without altering results.