Stability and structure-preserving numerical analysis of a stochastic delayed pine wilt disease model

, while the endemic equilibrium is assessed through delay-dependent local stability. The stochastic model includes multiplicative environmental noise and is shown to possess positive solutions with bounded first moments. Exact Itô logarithmic identities demonstrate that long-term infection behaviour depends on current and delayed host-vector states. A delay-aware stochastic nonstandard finite difference scheme is constructed using delayed indices, nonstandard denominator functions, and positive stochastic exponential factors. Numerical experiments illustrate the effects of delay, noise, and step size, with the proposed scheme showing controlled behaviour at larger steps.