Sahneh Faryad Darabi, Vajdi Aram, Melander Joshua, Scoglio Caterina M
Department of Electrical and Computer EngineeringKansas State UniversityManhattanKS66506.
IEEE Trans Netw Sci Eng. 2017 Nov 2;6(1):16-30. doi: 10.1109/TNSE.2017.2770091. eCollection 2019 Jan 1.
People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among [Formula: see text] possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold-a characteristic measure of a contact network robustness against epidemics-in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.
人们改变身体接触方式作为对传染病传播的预防反应。然而，只有少数数学模型考虑了疾病传播和接触适应过程的耦合动态。本文提出了一个模型，其中每个主体都有一个默认的接触邻域集，并且一旦主体对其默认接触中的感染情况变得警觉，就会切换到不同的接触集。由于每个主体可以采用两种可能的邻域集中的任何一种，整体接触网络会在[公式：见原文]种可能的配置之间切换。值得注意的是，一种两层网络表示可以完全对潜在的适应性、状态依赖接触网络进行建模。接触适应以非线性方式影响疾病流行规模和流行阈值（接触网络对流行病鲁棒性的一种特征度量）。特别地，所提出的自适应接触网络的流行阈值属于一个非线性佩龙 - 弗罗贝尼乌斯（NPF）问题的解，该解并不单调依赖于接触适应率。此外，网络适应模型预测了一种违反直觉的情况，即如果接触适应不够快，自适应改变接触可能会对网络抵抗流行病传播的鲁棒性产生不利影响。一类NPF问题的一个原创结果促进了本文的分析进展。
