A sensitivity analysis of a gonorrhoea dynamics and control model

Louis Omenyi, Aloysius Ezaka, Henry O. Adagba, Gerald Ozoigbo, Kafayat Elebute

wrongmedium confidenceCounterexample detected

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

Audit review

The paper’s controlled model (2.2) injects susceptibles directly into the infectious class at rate θ S (1−k2), independent of I, while also sending θ S I into the latent class. At the purported disease-free equilibrium E0 = (Q*, S*, 0, 0, 0, 0), one has dI/dt = θ S*(1−k2) > 0 for generic parameters, so E0 is not an equilibrium of (2.2). Nevertheless, the paper computes R0/Re via the next-generation method and presents local/global stability claims around this non-equilibrium point, rendering those claims invalid. The candidate solution identifies this inconsistency, provides a concrete counterexample with R0<1 but dI/dt|E0>0, and explains how to repair the model (e.g., remove the constant infection term or set k2=1) so that standard threshold/global stability results apply. Therefore, the paper’s main stability claims are wrong as written; the model’s critique is correct.

Referee report (LaTeX)

\textbf{Recommendation:} reject

\textbf{Journal Tier:} note/short/other

\textbf{Justification:}

The manuscript’s principal stability claims rely on a disease-free equilibrium that is not an equilibrium of the stated controlled model: dI/dt contains a constant source θ(1−k2)S that remains positive at (L,I)=(0,0). The next-generation computation, local Jacobian analysis, and Lyapunov proof are consequently invalid as presented. The model requires structural correction (or the explicit assumption k2=1) and a full re-analysis. As these issues touch the core results, incremental edits cannot salvage the current version.