Global analysis of a spatiotemporal cellular model for the transmission of hepatitis C virus with Hattaf-Yousfi functional response

Alexis Nangue, Bruno Nde Tchiffo

correctmedium confidence

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

Audit review

The paper’s PDE model, R0 expression, and stability results match the candidate’s conclusions. Both establish: existence/uniqueness of spatially homogeneous equilibria with a threshold R0, local stability of the uninfected state E0 when R0 ≤ 1, global stability of E0 under the stricter τ0 < 1 condition, and global stability of the infected equilibrium E* under u = 0, α0 = 1, α3 = α1α2 when R0 > 1. The candidate uses a Metzler-matrix argument for linearization and entropy-type Lyapunov functionals; the paper uses eigenmode/Routh–Hurwitz analysis and Hattaf–Yousfi-type Lyapunov constructions. A caveat: the paper’s abstract and conclusions overstate global stability of E0 at R0 ≤ 1, whereas the proven theorem requires τ0 < 1 (with R0 ≤ τ0), see the model equations and setting, the R0 derivation, the E0 global-stability theorem, and Theorem 8 for E* respectively in , , , and ; note the overstatement in the abstract/conclusion in and .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript presents a rigorous global analysis of a reaction–diffusion HCV model with generalized incidence and absorption. It establishes well-posedness, a clear R0 threshold, and global stability of both uninfected and infected equilibria (under stated structural conditions). The mathematics is sound and contributes to PDE epidemic modeling. Minor revisions are needed to align the abstract/conclusion with the proven global-stability condition (τ0 < 1) and to add brief clarifications to the Lyapunov/LaSalle arguments.