Spatial pattern regulation in pine wilt disease models with feedback mechanisms

Pine wilt disease is one of the most hazardous and devastating forest biological disasters in China. By causing large-scale mortality of pine trees, it not only leads to significant direct economic and ecological losses but also severely undermines the carbon sequestration capacity and carbon sink function of forest ecosystems. Since longhorns are the primary vectors of pine wilt disease, we investigate a susceptible-infected longhorn population model with memory-based diffusion and a state-feedback mechanism on a square domain. By analyzing the distribution of the characteristic roots of the system, we first derive conditions for system stability and the occurrence of Hopf bifurcation. Then, using time delay as a parameter, we apply the multiple time scales method to analyze the proposed model and derive the amplitude equation near the Hopf bifurcation point. Our results show that suitable adjustments of the feedback and memory-based diffusion parameters shift the aggregation pattern of longhorns from the center to the corners, which may help reduce infestation pressure in the core forest area.