A novel analysis approach of uniform persistence for a COVID-19 model with quarantine and standard incidence rate

The paper proves uniform persistence for the SEIAQR system with standard incidence when Rc>1 and provides explicit lower bounds with T = max{T1+T2, α} (Theorems 4.2–4.3), together with the formulas for T1, T2, and α and the componentwise bounds for S,E,I,A,Q,R. The candidate solution reproduces the same window-minimum/variation-of-constants framework: (i) positivity and Ṅ=λ−dN, (ii) a baseline lower bound for S, (iii) a sliding-window estimate relating I and A to the minimum of E, and (iv) a contradiction argument forcing E to stay above a positive threshold, from which bounds for I,A,Q,R follow. Minor differences are not substantive: the candidate compresses the paper’s auxiliary lemmas (notably Lemmas 4.1–4.3) and asserts S/N ≥ 1/(ηRc) via a stated T2 rather than re-deriving it, but this is exactly what Lemma 4.1 and the definitions of T2 and α guarantee in the paper. The conclusions and structure align with Theorems 4.2–4.3 and the model formulation in the paper.