Simplicial SIR rumor propagation models with delay in both homogeneous and heterogeneous networks

In social systems, not only do many interactions take place between pairs of individuals, but also take place in groups of individuals. To model the rumor propagation with consideration of both the pairwise interactions and the collective interactions, the simplicial SIR rumor propagation models are proposed in this paper. In addition, we take into account network topology and the time delay in the proposed models. Through analysis, the bistable phenomenon appears, in which the healthy and the endemic state can co-exist. The conditions for the existence and stability of the rumor persistent equilibrium point are obtained by theoretical analysis in homogeneous and heterogeneous networks. Moreover, the conditions under which the phenomenon of bifurcation occurs are given. To demonstrate the validity of the theoretical analysis, the proposed models are numerically simulated on homogeneous and heterogeneous networks.& COPY; 2023 Elsevier B.V. All rights reserved.