PERMANENCE AND UNIFORM ASYMPTOTIC STABILITY OF POSITIVE SOLUTIONS OF SAIQH MODELS ON TIME SCALES

The paper’s main claim (existence and uniform asymptotic stability of a unique almost periodic solution under H1–H2) is largely plausible but its proof has gaps on general time scales: earlier permanence/boundedness steps invoke Lemma 1 without verifying the necessary regressivity (−α ∈ R+), which fails on Z when parameters are large; moreover, the proof of Theorem 6 mixes an exogenous almost periodic λ(t) (H1) with a state-dependent λ via λ̂(t), and B-constants that explicitly depend on β, lA, lH. The model’s fixed-point solution is sound if one adds the standard regressivity assumption for the linear part, but it includes an incorrect “remedy” that claims B/A remains <1 after shrinking the linear coefficients to enforce regressivity—this need not hold, especially on discrete time scales. In short: both approaches need explicit, corrected time-scale regressivity hypotheses and a consistent treatment of λ(t).