<p>Wildfires pose a serious threat to humans, animals, ecosystems and infrastructure. The complex and uncertain interactions in wildfire spread between environmental conditions, human activities, and inherent randomness make it difficult to rely solely on a deterministic modeling approach. This study presents a novel stochastic mathematical model that incorporates environmental variability, including rainfall and wind effects as well as human intervention to capture the dynamics of wildfire spread. The basic reproduction number and equilibrium points of the deterministic model is investigated. The model has two equilibrium points, namely fire-free and active-fire equilibria. For the stochastic model, we first establish the existence of a unique and globally positive solution. Further, threshold parameter for the stochastic model is derived to quantify the potential of wildfire transmission. The criteria for the persistence and extinction of wildfire spread is analyzed using probabilistic techniques. These techniques identify critical thresholds that govern extinction or sustained fire spread under random disturbances. Moreover, the numerical solution of the stochastic model is obtained using high order spectral collocation technique, while a deep recurrent neural network is employed as a data-driven surrogate to forecast wildfire dynamics under stochastic conditions. Comparative analysis demonstrates close agreement between numerical and neural network predictions with mean absolute and mean squared errors consistently ranging from 10⁻³ to 10⁻⁸, indicating high predictive accuracy and stable convergence. These results confirm that the proposed framework provides a reliable and efficient tool for predicting wildfire dynamics and can be extended to the modeling of other complex natural hazards. Unlike existing wildfire models, this work integrates stochastic modeling with deep recurrent neural networks, enabling accurate prediction of wildfire dynamics under uncertainty.</p>