2008.06023
A Dynamical Framework for Modeling Fear of Infection and Frustration with Social Distancing in COVID-19 Spread
Matthew D. Johnston, Bruce Pell
incompletemedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper and the model agree on the threshold structure, equilibrium formulas, and local stability/instability conclusions for the disease-free and endemic equilibria, and both use essentially the same linearization/Routh–Hurwitz toolkit. However, for the two-delay model, the paper does not rigorously prove the Hopf bifurcation (it is presented as suggested by numerics), and the model’s solution likewise does not verify the first Lyapunov coefficient, so existence and nature of nearby limit cycles are not fully established in either source.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The study presents a timely reduced SEIR behavior–perception model capturing disease–behavior feedback. The core equilibrium and stability results for the disease-free and endemic states are clearly derived and consistent with the literature. However, the manuscript claims (via tables/theorems) sustained oscillations for the two-delay model while later acknowledging that the Hopf bifurcation remains unproved. Firming up this aspect (or tempering the claims) is necessary for correctness. Clarifying the Jacobian structure and consolidating seemingly inconsistent statements between the main text, tables, and appendix will improve clarity.