Composite Effective Degree Markov Chain for Epidemic Dynamics on Higher-Order Networks

Epidemiological models based on traditional networks have made important contributions to the analysis and control of malware, disease, and rumor propagation. However, higher-order networks are becoming a more effective means for modeling epidemic spread and characterizing the topology of group interactions. In this article, we propose a composite effective degree Markov chain approach (CEDMA) to describe the discrete-time epidemic dynamics on higher-order networks. In this approach, nodes are classified according to the number of neighbors and hyperedges in different states to characterize the topology of higher-order networks. By comparing with the microscopic Markov chain approach, CEDMA can better match the numerical simulations based on Monte Carlo and accurately capture discontinuous phase transitions and bistability phenomena caused by higher-order interactions. In particular, the theoretical solution to CEDMA can well predict the critical point at continuous phase transition and corroborate the existence of the discontinuous phase transition in the susceptible–infectious–susceptible (SIS) process. Moreover, CEDMA can be further extended to depict the susceptible–infectious–recovered (SIR) process on higher-order networks.