The increasing strength of higher-order interactions may homogenize the distribution of infections in Turing patterns

The spatial pattern of epidemic is one key metric describing epidemiological spread features, beneficial to formulation of the intervention measures. Networked reaction-diffusion (RD) systems have become popular to mathematically portray such patterns due to discrete distribution of human habitat. However, most of the current research focused on diffusion along pairwise interactions. Effect of diffusion along higher-order interactions is still understood poorly. To this end, in the paper, based on one classic SIR epidemic RD model, we study its Turing instability in simplicial complexes and analyze the impact of the simplex strength on Turing patterns. It is found by theoretical analysis and simulation that the distribution of infections in patterns tends to become homogeneity with the increase of the simplex strength, i.e., infection density of most nodes concentrates near the steady state. Obviously, for a newly emerging epidemic, such homogeneous scenario is unfavorable to epidemic control. Because it may lead to the decentralized allocation of limited resources, which is not enough to contain epidemic. In contrast, heterogeneous scenario that nodes with low and high infection density prominently distribute in two sides of steady state allows to put all limited resources into the targeted treatment of nodes with high infection density. Our findings link epidemic control with higher-order interactions and may provide a new insight into intervening epidemic from higher-order networks.