Advanced and comprehensive research on the dynamics of COVID-19 under mass communication outlets intervention and quarantine strategy: a deterministic and probabilistic approach

Driss Kiouach, Salim El Azami El-idrissi, Yassine Sabbar

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:55 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s deterministic and stochastic analyses are largely consistent and correct: R0 is computed via the next-generation approach (with the media term vanishing at the DFE), DFE is locally (R0<1) and globally (on S) stable, DFE becomes unstable and a unique endemic equilibrium exists when R0>1, and the stochastic extinction/persistence criteria are carefully derived. By contrast, the candidate solution incorrectly drops the media-coverage saturation factor in the steady-state equations when deriving the endemic equilibrium, yielding an explicit E* formula that omits β2 and b and therefore does not solve the paper’s model. Other parts of the candidate solution (global DFE stability via a linear Lyapunov functional; stochastic extinction and persistence arguments) are broadly sound but do not repair the endemic-equilibrium error.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The manuscript presents a thorough deterministic and stochastic analysis of a COVID-19 SQEAIHR model with quarantine and media coverage. The derivations of R0, the DFE thresholds, endemic equilibrium existence/uniqueness for R0>1, and the stochastic extinction/persistence criteria are technically sound and well organized. The use of Varga’s theorem to link α(F−V) and ρ(FV−1) streamlines the local stability analysis, and the stochastic part leverages clean logarithmic Lyapunov functionals with martingale SLLN. I recommend minor revisions to clarify the splitting used in the next-generation method (why β2,b do not appear in R0) and to more explicitly state the hypotheses ensuring uniform persistence.