Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal

Faïçal Ndaïrou, Delfim F. M. Torres

wronghigh confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 2 claims global asymptotic stability of the single DFE point (N,0,0,0,0,0,0,0) for R0<1, using a linear Lyapunov function and LaSalle. After deriving CD^αV ≤ κ v_i v_p v_h (R0−1) E, it identifies the set {CD^αV=0} with E=I=P=H=0, then asserts “from biological considerations” that this forces A=R=F=0 and S=N, hence concluding convergence to the unique DFE . This step is incorrect: E=I=P=H=0 implies A,R,F are constant, not necessarily zero; the largest invariant set is the full disease-free manifold {E=I=P=H=0, S+A+R+F=N}. The model solution correctly proves extinction of infection (E,I,P,H→0) for R0<1 and convergence to that manifold, not necessarily to the single DFE point. The system and R0 used match the paper’s model and formula .

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript’s modeling framework and Lyapunov construction are well done and valuable. However, the main theorem overstates the conclusion: the LaSalle invariant set is not the singleton DFE but the entire disease-free manifold where E=I=P=H=0 and S,A,R,F are constant. The final step relies on an unjustified biological assumption to collapse this manifold to the DFE. The paper should be revised to state and prove the correct global result (extinction of infection and convergence to the disease-free manifold) and to clarify assumptions and invariance arguments.