Global dynamics of a COVID-19 model with asymptomatic infections and quarantine measures

The paper establishes global dynamics for the long-term SEIAQR model (1) with standard incidence and Rc given in (3) . It proves that V0 is globally asymptotically stable for Rc<1 and globally attractive for Rc=1 using a limit system and a Lyapunov function L that includes an S-term (eqs. (9)–(10)) , and that the endemic equilibrium V* is globally asymptotically stable on Ω={E(0)>0} for Rc>1 via a Volterra-type Lyapunov function (eqs. (11)–(12)) and ω-limit set arguments . The candidate solution reaches the same threshold and stability conclusions with a different route: a direct Lyapunov function on infected classes for the DFE and a Volterra-type function for the EE with weights that, when evaluated at V*, coincide with those used in the paper. One minor flaw is that the candidate asserts, for Rc=1, that V̇=0 implies S=N and Y=0; in fact V̇=0 for all E=I=A=0 regardless of S, so the “largest invariant subset of {V̇=0} is {V0}” claim is not literally correct, though the conclusion still follows by analyzing the dynamics on the disease-free manifold. Aside from this, the reasoning aligns with the paper’s results and techniques.