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The paper’s nondimensional SIR-like system Ṡ* = (1−δ)I* − r0 S* I* − a S*, İ* = a S* + r0 S* I* − I*, Ṙ* = δ I* is exactly the model analyzed by the candidate solution . For a > 0 and δ > 0, both conclude the unique steady state is (S*, I*, R*) = (0, 0, 1) . For δ = 0, both derive the same quadratic and give the admissible equilibrium with explicit formulas for S*0 and I*0 (paper’s Eqs. (13)–(14); model’s identical expressions) . For a = 0 and δ > 0, both obtain the same final-size transcendental relation r0 (R∞ − 1) − δ + 1 = (1 − r0 − δ) e^{− r0 R∞ / δ} and identify a transcritical threshold at r0 = 1 with R∞ = 0 for r0 < 1 and a unique R∞ > 0 for r0 > 1 . The candidate adds standard dynamical-systems details (positive invariance, Jacobian linearizations) that the paper states informally; the only overreach is a brief global-stability remark for the a > 0, δ > 0 case that is not rigorously justified in the writeup. Otherwise, the arguments and results match.