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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. [ABSTRACT FROM AUTHOR]

In this paper, we propose a social contagion model with group interactions on heterogeneous network, in which the group interactions are represented by incorporating higher-order terms. The dynamics of the proposed model are analyzed, revealing the effect of group interactions on the system dynamics. We derive a global asymptotically stability condition of the zero equilibrium point. If the parameters enhancement factor and transform probability meet the condition, the social contagion will eventually disappear. The bifurcation behavior arising from group interactions is investigated, when the enhancement factor exceeds a threshold, the system undergoes a backward bifurcation. This implies that R 0 < 1 does not guarantee the disappearance of social contagion, we also need to control the initial values of social contagion at a lower level. The optimal control strategies for the model are provided. Moreover, the numerical simulations validate the accuracy of the theoretical analysis. It is worth noting that the group interactions lead to the emergence of a bistable phenomenon, in which the social contagion will either fade away or persist eventually, depending on the initial values. • The simplicial SIS social contagion model with delay is proposed on heterogeneous networks. • The dynamics of the model are analyzed, revealing the effect of group interactions on the system dynamics. • An optimal control strategy is proposed for the model, incorporating group interactions. [ABSTRACT FROM AUTHOR]