Coupled Propagation Dynamics Based On Multilayer Network With Simplicial Complexes

The epidemic spreading dynamics on complex networks has always been a hot topic for research,and it is associated with many factors,such as information diffusion,resources allocation,vaccination and so on.These elements interact with each other and coevolve during disease propagation.Therefore,it is essential to establish a suitable model of disease transmission.At present,most scholars construct a multilayer network model to explore the influence of various factors on the spread of disease.In previous studies,most of the coupling spreading models between diseases and information or resources focus on pairwise interaction,ignoring the non-pairwise or higher-order interplay among individuals in real life.Therefore,this paper will concentrate on the influence of the coupled transmission of information,resources and disease by using a two-layer network model based on simplicial complexes.The main innovation of the paper includes the following two parts:(1)Based on the simplicial complex,we propose a network propagation model to research the co-evolution of resources and diseases.The model consists of two networks,where the upper layer denotes the resource layer created with random simplicial complexes,representing the diffusion process of resources;the lower layer stands for the disease layer,describing the transmission process of disease.There are two possible states for nodes in the resource layer: the resource and no-resource state,which would determine the recovery probability of infected nodes in the disease layer.The infected nodes with resources can recover faster than the infected nodes without resources.At the same time,in the disease layer,the susceptible nodes will automatically generate resources,while the infected nodes would not.According to the microscopic Markov chain(MMC)method,the analytical epidemic threshold formula is obtained.Through numerous Monte Carlo(MC)simulations,it is verified that the experimental results obtained by MMC method and MC simulations are matched well,which means the model can predict the coupling spreading between disease and resources accurately.The conclusion shows that the introduction of2-simplex in the resource layer increases the probability and mode of the node and suppresses the spread of the disease.In addition,there is a threshold value for the resource,and the resource can be more effective for controlling the disease if it is less than the threshold.(2)Based on the simplicial complex,we propose a disease-information coupling spreading model with two kinds of competitive information.It consists of two networks,where the upper layer represents the diffusion network of disease-related information,generated with random simplicial complexes;the lower layer is used as the disease transmission network.There are two possible states for nodes in the information layer: the positive information and the negative information state,which determine the disease transmission probability of the lower node,and the positive information state makes this probability much lower than the probability in the negative state.In this paper,the disease outbreak threshold of this model is obtained by MMC method and the Monte Carlo(MC)simulation is used to verify the effectiveness of this method.Experiments show that the outbreak of positive(negative)information will inhibit the diffusion of negative(positive)information.Meanwhile,introducing 2-simplex in the propagation of positive information can increase the probability of obtaining positive information for nodes,inhibiting the outbreak and propagation of disease,while the negative information is opposite,and the effect of2-simplex is stronger on positive information than negative information.Finally,we made a comparative study of the effects of the attenuation factor and the 2-simplex,and found that the attenuation factor is more obvious in raising the threshold of disease outbreak and inhibiting disease transmission than the 2-simplex.