SIS Epidemic Propagation on Scale-Free Hypernetwork

The hypergraph offers a platform to study structural properties emerging from more complicated and higher-order than pairwise interactions among constituents and dynamical behavior, such as the spread of information or disease. Considering the higher-order interaction between multiple nodes in the system, the mathematical model of infectious diseases spreading on simple scale-free networks is extended to hypernetworks based on hypergraphs. A SIS propagation model based on reaction process strategy in a universal scale-free hypernetwork is constructed, and the theoretical and simulation analysis of the model is carried out. Using mean field theory, the analytical expressions between infection density and hypernetwork structure parameters as well as propagation parameters in steady state are given. Through individual-based simulation, the theoretical results are verified and the infectious disease spread process under the structure of the hypernetwork and simple scale-free network is compared and analyzed. It becomes apparent that infectious diseases are easier to spread on the hypernetworks, showing the clear clustering characteristics of epidemic spread. Furthermore, the influence of the hypernetwork structure and model parameters on the propagation process is studied. The results of this paper are helpful in further studying the propagation dynamics on the hypernetworks. At the same time, it provides a certain theoretical basis for the current COVID-19 prevention and control in China and the prevention of infectious diseases in the future.