New mechanism for spatial heterogeneity pattern revealed by nonlocal competition and host-taxis in a 2D pine wilt...

Different from the existing studies on the influence of self-diffusion or cross-diffusion on Turing instability, this paper originally focuses on the effect of nonlocal competition and host-taxis on Turing instability in a more realistic two-dimensional space, and novelly applies it to study the control of pine wilt disease. It turns out that the incorporation of host-taxis is not conducive to the generation of Turing instability, whereas nonlocal competition can promote the formation of pattern structure by facilitating the occurrence of it. The results not only reveal the new mechanism for the emergence of spatial heterogeneity patterns, but also provide an alternative theoretical explanation for the actually observed multi-point aggregation and multiple outbreaks of pine wilt disease. The various spatial patterns induced by nonlocal competition and host-taxis are numerically illustrated. We find that the Turing patterns can preserve the symmetry of the initial distribution, and contrary to the taxis diffusion, the self-diffusion of D. helophoroides promotes the pattern formation. Furthermore, the high consistency between the simulated and actual distribution patterns of pine wilt disease strongly validates the practical reference value of the paper. The most interesting finding is that we obtain the circular aggregation distribution pattern from simulations, which is consistent with the actual spread trend of pine wilt disease, and our study theoretically reveals the intrinsic evolution mechanism behind its occurrence.