Model for prognostic of symptomatic, asymptomatic and hospitalized COVID-19 cases with correct demography evolution

The paper proves global asymptotic stability of the disease-free manifold (CFM/DFM) for the SEIAHR model when R0 < 1 by (i) isolating the infectious block (E,I,A), (ii) comparing it to a cooperative linear system y' = My with M Metzler, using a comparison theorem, and (iii) invoking that R0 < 1 implies all eigenvalues of M have negative real part, so z(t)=e^{Mt}z(0)→0 and hence y(t)→0; then H(t) decays by linear forcing from I(t) (Theorem 3) . The model solution follows the same strategy: it constructs a worst-case constant system with S/N replaced by 1, uses positivity of the semigroup for Metzler matrices, and the next-generation threshold (R0 = ρ(FV^{-1}) < 1) to conclude s(F*−V)<0 and exponential decay, plus the linear H-equation, yielding GAS of the DFM. The R0 expression in the model matches the paper’s formula exactly (βσ((1−p)γ + pk1 + μ)/((γ+μ)(k1+μ)(σ+μ))) . Thus both are correct and essentially the same proof, with minor differences in presentation and citations.