2202.02993
Global stability of multi-group SAIRS epidemic models
Stefania Ottaviano, Mattia Sensi, Sara Sottile
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves, for the multigroup SAIR case (γ=0), that if R0>1 then there is a unique endemic equilibrium and it is globally asymptotically stable, using: (i) next-generation matrix to compute R0; (ii) a monotone, strictly sublinear fixed-point map for existence/uniqueness; and (iii) a Volterra-type Lyapunov function combined with the graph-theoretic cycle condition and LaSalle’s invariance principle for global stability. These are precisely the steps the candidate solution outlines, with matching formulas for the next-generation matrix and the fixed-point reduction, and the same graph-theoretic Lyapunov strategy for SAIR. See the paper’s Lemma 2 and equation (6) for R0, Theorem 9 for uniqueness via a strictly sublinear fixed-point, and Theorem 14 with its graph-theoretic construction for SAIR global stability .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The analysis delivers correct and useful global results for a multigroup SAIR(S) model with asymptomatic and symptomatic transmission, leveraging established threshold and Lyapunov techniques. The SAIR global stability theorem is clean and well-motivated. A few expository improvements (clearer statement of assumptions; more explicit Lyapunov weight construction) would enhance accessibility, but the mathematical content is sound and contributes to the specialist literature.