Epidemic spreading on spatial higher-order network

Higher-order interactions exist widely in mobile populations and are extremely important in spreading epidemics, such as influenza. However, research on high-order interaction modeling of mobile crowds and the propagation dynamics above is still insufficient. Therefore, this study attempts to model and simulate higher-order interactions among mobile populations and explore their impact on epidemic transmission. This study simulated the spread of the epidemic in a spatial high-order network based on agent-based model modeling. It explored its propagation dynamics and the impact of spatial characteristics on it. Meanwhile, we construct state-specific rate equations based on the uniform mixing assumption for further analysis. We found that hysteresis loops are an inherent feature of high-order networks in this space under specific scenarios. The evolution curve roughly presents three different states with the initial value change, showing different levels of the endemic balance of low, medium, and high, respectively. Similarly, network snapshots and parameter diagrams also indicate these three types of equilibrium states. Populations in space naturally form components of different sizes and isolations, and higher initial seeds generate higher-order interactions in this spatial network, leading to higher infection densities. This phenomenon emphasizes the impact of high-order interactions and high-order infection rates in propagation. In addition, crowd density and movement speed act as protective and inhibitory factors for epidemic transmission, respectively, and depending on the degree of movement weaken or enhance the effect of hysteresis loops.