Pattern dynamics analysis and application of West Nile virus spatiotemporal models based on higher-order network topology.

The higher-order network structure characterized by hypergraphs or simplicial complexes has become a research hotspot in network space. In this paper, a simplicial complex is used to describe the multivariate interaction between populations, and the reaction diffusion equation in higher-order organization is established. Under certain constraints, the Turing instability condition of the system is derived. Then, the advection mechanism is introduced to construct a reaction-diffusion model with directional migration mechanism, and the pattern dynamics of the reaction-diffusion-advection equation is systematically analyzed on two-dimensional torus and triangular lattice networks. In addition, in the numerical simulation part, it is found that the spatial density distribution in the stable patterns of the two populations is anti-phase. At the same time, we verify that the diffusion of the population depends on the topological structure and coupling, and conclude that the higher-order interaction on the triangular lattice network has a greater influence on the Turing instability than the higher-order Erdos-Renyi (ER) network. In the system process of simulating the existence of advection mechanism, the triangular lattice network will increase the spatial heterogeneity of the pattern due to the existence of directional migration mechanism. In the absence of diffusion, the increase of directional movement intensity will also cause Turing instability. Finally, the reaction-diffusion model in higher-order organization is applied to practice, and the validity of the model is verified.