Spatiotemporal Dynamic Analysis of Delayed Diffusive Pine Wilt Disease Model with Nonlocal Effect

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1312-1336, August 2024.
Abstract. Pine wilt disease is one of the most serious forest diseases and pests in China, which seriously influences the realization of the goal of “carbon peak and carbon neutrality.” In our article, we divide longhorns into susceptible ones and infected ones since pine wilt disease is spread by longhorns. Considering the saturation incidence of pine wilt disease, we establish a delayed reaction-diffusion model with nonlocal effect for susceptible and infected longhorns. First, we consider the well-posedness of solutions and the type of equilibria for the nonspatial system. Next, we discuss the dynamics of the spatial system with nonlocal effect. According to the multiple time scales method, we derive the normal form of Hopf bifurcation for a system associated with nonlocal effect, and the stability and direction of bifurcating periodic solutions are analyzed. Finally, using real data for China to perform data analysis, we select suitable values of parameters. Numerical simulations are presented to illustrate the ecological significance. Combined with the current situation, we provide some theoretical support for the prevention and control of pine wilt disease in China. Especially, we find that the nonlocal term can induce spatially stable inhomogeneous bifurcating periodic solutions.