Unraveling pine wilt disease: Comparative study of stochastic and deterministic model using spectral method

The pinewood nematode, which causes a disease known as pine wilt, is a serious threat to pine forests all over the world. In this paper, we analyze the dynamics of pine wilt disease and its effects on forest ecosystems using mathematical modeling of pine wilt disease, its numerical simulations, and analytical techniques. Understanding the nematode's spread, evaluating the efficiency of management efforts, and foreseeing the long-term effects on pine populations are some of our research's goals. To gain a comprehensive understanding of the dynamics of the disease, we categorize pine trees and vectors systematically into susceptible, exposed, and infected groups. We first presented disease dynamics through a flow diagram which is then transformed to system of ordinary differential equations along with non-negative initial conditions. The deterministic model is then transformed to a stochastic model. Using both deterministic and stochastic modeling approaches, this study explores the complex transmission dynamics of Pine Wilt disease. Basic reproduction number has been calculated via next generation technique and some cases of stability analysis on the basis of the values of reproduction number has been discussed. For the solution of stochastic model Legendre Spectral collocation method has been used as it is known for its high accuracy in approximating solutions to complex stochastic models. It can achieve exponential convergence rates, making it suitable for problems where high precision is required. The results of both deterministic and stochastic models are compared via different figures. We find crucial thresholds for disease transmission and highlight significant factors affecting the spread of diseases through simulations. Our research shows that preventing the severe impacts of pine wilt disease requires early detection and intervention. Additionally, our mathematical model is a useful tool for enhancing disease management plans. This research advances our knowledge of the dynamics of the pine wilt disease and provides useful advice for managing forests and promoting conservation. Our research highlights the need for quick action to protect pine forests from this harmful virus.