Global stability and optimal control in a dengue model with fractional order transmission and recovery process

The paper and the candidate solution agree on the invariant region, threshold R0, and the existence and stability of disease-free and endemic equilibria, but both proofs lean critically on an approximation (their Theorem 2.1) to replace the tempered Riemann–Liouville terms by constant-coefficient ODE terms. The paper then proves global stability for the ODE surrogate and states the result for the original fractional system without establishing a rigorous equivalence; the model solution follows the same path (next-generation matrix on the approximated system, Routh–Hurwitz, Li–Muldowney) with different technical details but the same gap. Hence, the conclusions are plausible and consistent, but the logical bridge from the fractional system (4.8) to the ODE system (5.43)/(⋆) is not fully justified.