| In recent years,with the rapid development of complex systems and complexity science,network science,as an emerging multi-field interdisciplinary subject,has attracted the extensive attention of experts and scholars in various fields of academia.The traditional network only focuses on the interaction between pairs of nodes,and it is difficult to describe the group interaction that is common in complex systems such as social,biological and technological networks.Therefore,the high-order network becomes the new frontier of network science research.As a manifestation form of higher-order network,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.The hyperedge of hypergraph contain any number of nodes,which can accurately represent all kinds of complex and multi-dimensional relationships in real networks.For the modeling of complex systems,the introduction of high-order interaction can describe the interaction closer to reality in many scenes,so as to reproduce the phenomenon that cannot be reproduced in the previous models in the simulation experiments.In this paper,relevant theories such as complex network,hypergraph theory,stochastic process theory and average field theory are comprehensively applied,and hypernetworks based on hypergraphs and disease spread models are taken as the main research objects.The dynamic behavior mechanism of disease spread on two kinds of typical hypernetworks is deeply studied,in order to understand the law of high-order disease transmission on hypernetworks better.The specific research contents are as follows:(1)A disease spread model on scale-free hypernetworks.In this paper,the scalefree hypernetwork is used to describe the social contact relationship of individuals in the real society,and the hyperdegree distribution of the generated network is analyzed.Two kinds of disease spread models on the scale-free hypernetworks are constructed by using two different disease transmission mechanisms on the hypernetwork and combining with the SIS model in the disease transmission dynamics.The theoretical analysis and experimental verification of the global propagation model are given.Simulations were conducted to assess the influences of structural and propagation parameters of the hypernetwork on the spread speed and the steady-state outcomes of the disease.Besides,the different results of the disease spread on the ordinary complex network and the hypernetwork were compared,and the law of the disease spread in the scale-free hypernetworks was revealed from a macroscopic perspective.(2)A disease spread model on small-world hypernetworks.In this paper,the small-world hypernetwork is used to illustrate the contact relationship between individuals in the real world,and the aggregation coefficient and the average shortest path of the generated network are examined.Two kinds of disease spread models on the small-world hypernetworks are constructed by using two different disease transmission mechanisms on the hypernetwork and combining with the SIS model in the disease transmission dynamics.Through simulation experiments,the influences of structural parameters,propagation parameters and small-world characteristics of the network on the spread speed and steady-state results of the disease were analyzed.What’s more,the law of the disease spread in the small-world hypernetworks was revealed from a macroscopic perspective.(3)Study on immune characteristics and strategies of disease spread on hypernetworks.Based on the characteristics of the above two hypernetwork models and transmission strategies,the appropriate disease immunization strategies are proposed respectively: nodes immunization strategy under RP propagation model in scale-free hypernetwork and hyperedges immunization strategy under CP propagation model in small-world hypernetwork.The effectiveness of the immunization strategies proposed was verified by simulation experiments at last. |
