Higher-order non-Markovian social contagions in simplicial complexes

Abstract

Higher-order structures such as simplicial complexes are ubiquitous in numerous real-world networks. Empirical evidence reveals that interactions among nodes occur not only through edges but also through higher-dimensional simplicial structures such as triangles. Nevertheless, classic models such as the threshold model fail to capture group interactions within these higher-order structures. In this paper, we propose a higher-order non-Markovian social contagion model, considering both higher-order interactions and the non-Markovian characteristics of real-world spreading processes. We develop a mean-field theory to describe its evolutionary dynamics. Simulation results reveal that the theory is capable of predicting the steady state of the model. Our theoretical analyses indicate that there is an equivalence between the higher-order non-Markovian and the higher-order Markovian social contagions. Besides, we find that non-Markovian recovery can boost the system resilience to withstand a large-scale infection or a small-scale infection under different conditions. This work deepens our understanding of the behaviors of higher-order non-Markovian social contagions in the real world. High-order structures are ubiquitous in numerous real-world networks and play a significant role in social contagion phenomena, the authors introduce a novel higher-order non-Markovian social contagion model, addressing limitations of traditional models. Through mean-field theory and simulations, the authors demonstrate that there is an equivalence between the higher-order non-Markovian and the higher-order Markovian social contagions and reveal the resilience enhancement conferred by non-Markovian recovery, shedding light on real-world contagion dynamics.