Epidemic Population Games With Nonnegligible Disease Death Rate

Both the paper and the candidate solution use the same composite Lyapunov construction L(Y)=S(I,R,B)+S(x,p), the same control choice q̇=G=−∂BS(I,R,B), and derive the same key decay estimate d/dt L ≤ −P(x,p) − (B−δ) Ĩ^2 − a_B(ω−δI) R̃^2, cf. (18)–(21) and (24) in the paper . However, to conclude convergence via a LaSalle argument one must also prove q(t) is bounded. The paper explicitly flags this as a required step and sketches how to obtain it via (25) (using uniform bounds on Î_B, R̂_B, a_B and ∂Ba_B), but does not carry out the details; the candidate solution omits this step altogether . In addition, the paper’s Theorem 1 states GAS of e* without explicitly invoking Assumption 4, which the paper itself introduces earlier to ensure the uniqueness of x* for n≥3; the candidate solution correctly conditions uniqueness on n=2 or Assumption 4 . Thus, both arguments are structurally sound but incomplete as written.