Insights on Stochastic Dynamics for Transmission of Monkeypox: Biological and Probabilistic Behaviour

The paper’s Theorem 4.1 asserts almost-sure extinction of the infectious load when R0<1 and sketches a log–Itô argument, but it replaces the stochastic integrals ∫a_s dB_s by constants times Brownian motions B_i(t) and then invokes the strong law B_i(t)/t→0. That step is unjustified for general adapted integrands and leaves a gap. The candidate solution keeps the local martingale M(t)=∫a_s dB_s explicit, proves a self-contained strong law M(t)/t→0 a.s., and completes the argument. Aside from that martingale gap (and a likely sign typo in LU(t)), the drift bounds and the threshold definition match the paper. Therefore the result is correct but the paper’s proof is incomplete; the candidate solution is correct and fills the gap. See the model (1) and Theorem 4.1 statement in the paper, the log-Itô setup and the contested step using Brownian SLLN (detailed around equations (11)–(13)) .