ANALYSIS OF AN SIR–MODEL WITH GLOBAL AND LOCAL INFECTIONS

Thomas Götz

correcthigh confidence

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

Audit review

The paper derives the DFE, Jacobian, next-generation matrix, closed-form R0,p, and the transmission threshold β̃p; it also proves ρ*0=ρ*1=(γ+µ)/β and shows an interior minimum of ρ*(p). The candidate reproduces these steps with the same ξ=(I,Y), η=(S,X) split, identical Fp and Vp, the same formulae for R0,p and β̃p, and the same endpoint and interior behavior of ρ*. The only minor gap is that the candidate asserts S*0>S*1 heuristically rather than using the paper’s short algebraic argument, but the conclusion is the same. Overall, both are correct and procedurally aligned.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript rigorously analyzes a mixed global–local SIR pair-approximation model, deriving explicit expressions for R0,p and the transmission threshold β̃p and characterizing stability and endemic behavior. The presentation is clear, computations check out, and the discussion of the active-pair fraction is insightful. Minor clarifications around standard hypotheses (for next-generation/center-manifold arguments) would improve accessibility.