2104.12029
The SIR model of an epidemic
William G. Faris
correctmedium confidence
- Category
- Not specified
- Journal tier
- Note/Short/Other
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper derives dS/dR = −r0 S and the exponential relation S(R) = S0 e^{−r0 R}, then states the final-size equation 1 − R∞ = S0 e^{−r0 R∞} with a unique solution 0 < R∞ < 1, and notes that increasing r0 pushes R∞ closer to 1 . The candidate reproduces the same core derivation, adds a rigorous proof that I(t) → 0 and two routes to monotonicity in r0. Thus, both are correct and use materially the same argument, with the model adding minor rigor/details.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} note/short/other
\textbf{Justification:}
This is a clear and accurate exposition of the classical SIR final-size analysis. It derives the standard exponential S–R relation, final-size equation, uniqueness, and qualitative dependence on r0, aligning with the literature. Minor additions—a short proof that I(t)→0 and an explicit monotonicity proof for R∞(r0)—would make the presentation fully self-contained without changing any conclusions.