SIRSi-Vaccine dynamical model for Covid-19 pandemic

Cristiane M. Batistela, Diego P. F. Correa, Átila M Bueno, José R. C. Piqueira

incompletehigh confidence

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

Audit review

The paper correctly states the SIRSi‑Vaccine system, the disease‑free equilibrium (DFE) Pdf2, its Jacobian eigenvalues, and the threshold ω > (R0−1)(μ+γ) for DFE stability, as well as the endemic equilibrium Pe2 coordinates and its existence condition ω ≤ (R0−1)(μ+γ). However, it contains typographical misstatements around λ2/λ3 and labels Pdf2/Pe2, and does not provide an analytic proof of Pe2 stability (relying on numerics). The model solution reproduces the correct Jacobian, thresholds, and Pe2 coordinates, and identifies the transcritical coincidence at equality, but it also does not rigorously establish Pe2 local stability (no Routh–Hurwitz or center-manifold proof). Hence both are incomplete on the endemic point’s stability and the claimed full “interchangeable stability” proof.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work sets up a reasonable compartmental model and correctly identifies equilibria and threshold conditions, and it is well motivated by public-health concerns. However, the presentation contains typographical errors in the key stability discussion for the vaccine model and lacks an analytic proof of endemic equilibrium stability, despite making claims of interchangeable stability. The paper would benefit substantially from correcting these issues and supplying a rigorous stability analysis (or clearly framing the numerical nature of the claim).