Dynamical Analysis of Stochastic COVID-19 Model with Jump-Diffusion

The paper’s persistence theorem (Theorem 3) drops the −(ν+γ) term when passing from the log-I identity (Eq. (16)/(17)) to the averaged equality (Eq. (23)→(24)), and also mishandles division by t in Eq. (24). This yields the stated limits S̃, Ĩ, R̃ that violate the mass-balance identity derived from Eqs. (8)–(10) and Lemma 1(ii). In particular, the paper’s limits satisfy S̃+Ĩ+R̃=2(βΛ/ν−ϕ2)/β≠Λ/ν, whereas adding the model equations and letting t→∞ forces ⟨S⟩+⟨I⟩+⟨R⟩=Λ/ν (using Lemma 1(ii)). The candidate solution keeps the missing −(ν+γ) term, leading to self-consistent limits that do sum to Λ/ν, and follows the standard martingale LLN pathway the paper also invokes. See the paper’s Eqs. (16)–(18) for the correct log-I drift with −(ν+γ) present, the incorrect Eq. (23)/(24) where it disappears, and the statement of Theorem 3 with the inconsistent S̃, Ĩ, R̃.