Transmission dynamics and control measures of reaction–diffusion pine wilt disease model

The pine wilt disease is a serious and fatal disease that affects various species of pine trees worldwide. In this work, the conventional temporal-only model for pine wilt disease is extended to incorporate the spatial influences on the model dynamics. Firstly, the existence and uniqueness of the solution, along with its positivity and boundedness, are all investigated. Secondly, the stability of equilibrium points is analyzed for diffusive and non-diffusive versions of the model. The regions of stability in the space of key parameters are evaluated to explore possible control measures to conceal the spread of the disease and stabilize the disease-free equilibrium point. The possible occurrence of Turing -instability is examined for the present model. Two efficient schemes for the NSFD numerical method are employed to confirm theoretical results. The stability and convergence analysis of the two schemes is provided, followed by numerical experiments that cover different scenarios for the pine wilt disease dynamics.