Dynamics of an SIRWS model with waning of immunity and varying immune boosting period

Richmond Opoku-Sarkodie, Ferenc A. Bartha, Mónika Polner, Gergely Röst

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves: (i) DFE is LAS for R0<1 and loses stability for R0>1; (ii) no other equilibrium exists in D when R0≤1; (iii) a unique positive endemic equilibrium exists for R0>1; (iv) a forward transcritical bifurcation occurs at R0=1; and crucially (v) the endemic equilibrium’s local stability depends on parameters (α,ν) via the Routh–Hurwitz function yν(α)=a1a2−a3, which changes sign, producing Hopf bifurcations and stability switches (with explicit coefficients and a transformation establishing symmetry and zero contours) . The candidate solution correctly handles (i)–(iv) but incorrectly claims a1a2−a3>0 “manifestly,” implying LAS of the endemic equilibrium for all R0>1, which contradicts the paper’s analytic setup and numerical bifurcation evidence of Hopf instabilities and bistability regions .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

Analytical development (equilibria, DFE stability, forward transcritical bifurcation) is correct and clearly presented. The Routh–Hurwitz formulation yν(α)=a1a2−a3 is insightful and, together with numerical continuation, convincingly demonstrates Hopf bifurcations and bistability. Minor improvements to derivational transparency and reproducibility would further strengthen the presentation.