Dynamical Characterization of Antiviral Effects in COVID-19

The paper’s Theorem 4.1 correctly identifies the threshold R(t_tr) = 1 for efficacy and the qualitative behaviors (items ii–iv), but its item (i) asserts that the viral maximum occurs at t_tr for both p- and β-inhibition; this is only guaranteed for sufficiently strong p-inhibition because V̇ depends on p but not directly on β. The sketch proof relies on the approximation V̇ ≈ (R−1)δV and ignores the α(t) correction, which conflates sign changes at t_tr in the β-only case. The model’s solution improves the analysis with an exact second-derivative identity at stationary points, but it repeats the over-strong claim that the peak is at t_tr for β-inhibition and implicitly infers V̇(t_tr^+) < 0 from R(t_tr) < 1 without justification. Overall, both are close on the main qualitative picture but each misses crucial conditions at the intervention boundary.