FEAR-DRIVEN EXTINCTION AND (DE)STABILIZATION IN A PREDATOR-PREY MODEL INCORPORATING PREY HERD BEHAVIOR AND MUTUAL INTERFERENCE

The paper’s Theorem 5.1 (fear-driven finite-time extinction for some k>0, starting from initial data that converges to a stable coexistence equilibrium when k=0) is plausibly true, but its proof contains substantive gaps and inconsistent inequalities (e.g., replacing −bu^2 by −u^2, using an unproved upper bound u≤a to obtain a^2/(kv), and introducing a time-dependent bound that is then used uniformly in T*). The candidate model solution provides a rigorous, constructive sufficient condition and an explicit k via a standard sublinear change of variables z=u^{1−p}, but it only guarantees extinction under quantitative constraints relating (u0,v0) and parameters; it does not establish the paper’s stronger existence claim for arbitrary such initial data. Hence, the paper’s argument is incomplete, and the model’s solution, while mathematically correct as a sufficient criterion, is also incomplete relative to the paper’s stated claim.