Application of the criterion of Li-Wang to a five dimensional epidemic model of COVID-19. Part I

Both the paper and the candidate solution use Li–Wang via the second additive compound to infer Hurwitz stability at the disease-free equilibrium, but they each contain material gaps. In the paper, the Jacobian at the DFE is printed with a52=a53=0, contradicting the model’s d-equation and the earlier definition of Jp* (which has a52=β6 and a53=β5); the determinant formula is then derived from this mis-specified matrix, and Theorem 4.11(ii) asserts column-diagonal dominance of J[2]p0 under (a)–(d) without a correct column-by-column verification. Using the correct Jp0 and J[2]p0, one can produce parameters satisfying (a)–(d) (and the paper’s determinant hypothesis) for which the sixth column margin is negative, so J[2]p0 is not column-diagonally dominant. The candidate solution repeats the same dominance claim, omits β5 in the S5 column sum, and uses a loose bound to conclude m1>0. Hence both arguments are incomplete on the key dominance step, though the overall Li–Wang logic is otherwise standard.