Zhu Peican, Wang Xinyu, Li Shudong, Guo Yangming, Wang Zhen
School of Computer Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.
Technology and Centre for Multidisciplinary Convergence Computing, Northwestern Polytechnical University, Xi'an 710072, China.
Appl Math Comput. 2019 Oct 15;359:512-524. doi: 10.1016/j.amc.2019.02.049. Epub 2019 May 14.
Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. A two-layered multiplex network model (usually composed of a virtual layer sustaining unaware-aware-unaware (UAU) dynamics and a physical one supporting susceptible-infected-recovered-dead (SIRD) process) is presented to investigate the spreading property of fatal epidemics in this manuscript. Due to the incorporation of the virtual layer, the recovered and dead individuals seem to play different roles in affecting the epidemic spreading process. In details, the corresponding nodes on the virtual layer for the recovered individuals are capable of transmitting information to other individuals, while the corresponding nodes for the dead individuals (which are to be eliminated) on the virtual layer should be removed as well. With the coupled UAU-SIRD model, the relationships between the focused variables and parameters of the epidemic are studied thoroughly. As indicated by the results, the range of affected individuals will be reduced by a large amount with the incorporation of virtual layers. Furthermore, the effects of recovery time on the epidemic spreading process are also investigated aiming to consider various physical conditions. Theoretical analyses are also derived for scenarios with and without required time periods for recovery which validates the reducing effects of incorporating virtual layers on the epidemic spreading process.
众多努力都致力于研究孤立网络的网络活动和动态特性。然而，在实际中，大多数复杂网络可能相互连接（由于存在共同组件）并呈现分层特性，而不同层上的连接代表着各种关系。这类网络被称为多重网络。本文提出了一种两层多重网络模型（通常由维持无意识 - 有意识 - 无意识（UAU）动态的虚拟层和支持易感 - 感染 - 恢复 - 死亡（SIRD）过程的物理层组成）来研究致命流行病的传播特性。由于纳入了虚拟层，恢复者和死亡者在影响疫情传播过程中似乎扮演着不同的角色。具体而言，虚拟层上恢复者对应的节点能够向其他个体传递信息，而虚拟层上死亡者（即将被消除）对应的节点也应被移除。通过耦合的UAU - SIRD模型，深入研究了疫情相关变量和参数之间的关系。结果表明，纳入虚拟层后受影响个体的范围将大幅减少。此外，还研究了恢复时间对疫情传播过程的影响，以考虑各种实际情况。针对有无恢复所需时间段的情况进行了理论分析，验证了纳入虚拟层对疫情传播过程的减少作用。
