Stochastic Analysis of Pine Wilt Epidemic Model With Dynamically Consistent Approximation

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Abstract
The present study investigated the dynamics of the nonlinear stochastic pine wilt epidemic model. An extension of the stochastic to deterministic model is presented. Equilibria, positivity, boundedness, extinction, and disease persistence were studied rigorously. Standard and nonstandard numerical techniques like Euler–Maruyama, stochastic Euler, stochastic Runge–Kutta, and stochastic nonstandard finite difference are presented for computational analysis. Furthermore, the nonstandard method is a dynamically consistent approximation of stochastic differential equations of the pine wilt epidemic model that is efficient, low cost, and independent of time‐step size. The comparison section with standard methods strengthens the nonstandard method and supports the theoretical results of the model.
Funding Information
  • Princess Nourah Bint Abdulrahman University (PNURSP2025R371)
  • King Khalid University (RGP2/206/46)
  • King Faisal University (KFU241144)

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