警觉与疾病的传播次序性对动力学的影响

近年来，基于双层网络研究疾病传播与警觉传播的相互作用已引起广泛关注。在该模型框架下，疾病通过物理接触网络传播，而有关疾病的警觉信息则通过虚拟接触网络传播，两个网络具有相同的节点，但对应的连边不同。已有的模型在进行理论分析时，多假设警觉意识的传播先于疾病的传播(ordered model)，考虑到在真实情况下，疾病传播和警觉意识的传播难以区分先后顺序，因此该文提出了一种不考虑传播次序的模型(concurrent model)。通过研究发现，两种模型给出相同的疾病爆发阈值，但却给出不同的传播范围，当警觉意识传播率较小的时候，无序模型对应的感染范围会小于有序模型对应的感染范围，但是随着警觉意识传播率的增加，结果会发生反转，即无序性模型会导致疾病的感染范围大于有序性模型。

Effects of the Order of Awareness Diffusion and Disease Propagation on the Spreading Dynamics

Recently, studies on the interaction between disease transmission and awareness transmission based on two-layer networks have attracted much attention. Within such a framework, infectious disease is propagated through physical contact networks, while the diffusion of awareness is transmitted through virtual contact network. Moreover, the nodes on two layers are the same, but the edges connecting nodes in the two layers are different. Most of the existing models assume that the diffusion of awareness precedes the spread of disease (hereinafter referred to as ordered model). In real cases, it is difficult to distinguish the order of disease transmission from that of awareness diffusion, thus, this paper proposes a model without considering the order of two spreading processions (concurrent model for short). We find that the two models yield the same epidemic threshold, but have different influence on the spreading sizes. When the transmission rate of awareness is low, the epidemic size of concurrent model is smaller than that of ordered model. However, with the increase of the transmission rate of awareness, the result is reversed, that is, the epidemic size of the concurrent model is larger than that of ordered model.