Resilience patterns in higher-order meta-population networks

Meta-population networks are effective tools for capturing population movement across distinct regions, but the assumption of well-mixed regions fails to capture the reality of population higher-order interactions. As a multidimensional system capturing mobility characteristics, meta-population networks are inherently complex and difficult to interpret when subjected to resilience analysis based on N-dimensional equations. We propose a higher-order meta-population model that captures large-scale global cross-regional mobility and small-scale higher-order interactions within regions. Remarkably, we extend the dimension-reduction approach, simplifying the N-dimensional higher-order meta-population system into a one-dimensional equation by decomposing different network behaviours into a single universal resilience function, thereby allowing for convenient and accurate prediction of the system resilience. The network structure and human mobility parameters can clearly and simply express the epidemic threshold. Numerical experimental results on both real networks and star networks confirm the accuracy of the proposed dimension-reduction framework in predicting the evolution of epidemic dynamics on higher-order meta-population networks. Additionally, higher-order interactions among populations are shown to lead to explosive growth in the epidemic infection size potentially. Population mobility causes changes in the spatial distribution of infectious diseases across different regions.