Stochastic Epidemic-Economic Adaptive Network Dynamics

耦合网络的动态是理解全球危机的许多方面的关键，特别是关键过渡的性质-往往与崩溃有关-取决于基础网络的耦合。从这个角度来看，COVID-19疫情并不例外。社会（流行病传播）网络由个人（代理人/节点）组成，他们的社会联系形成链接，通过节点和链接的非平凡重叠耦合到许多经济网络，从而形成大规模的多层网络。这些结构通常不是静态的，而是适应性的，因为联系可能因动态而出现或消失。在这个项目中，我们建议研究接触过程作为一种现象发生在动态自适应多层网络，特别是耦合流行病和经济层。这个跨学科项目的重点是在理论物理和数学中使用的网络动力学的基础技术和方法，这些技术和方法有助于澄清此类系统中关键转变（崩溃或临界点）的性质。第一个方面是基于微分方程模型，我们的目标是开发新的方法，时刻关闭多层网络，然后我们通过设计具体的程式化的经济流行病模型进行测试。作为第二步，我们通过粗粒化外部多层输入作为单层的参数不确定性输入来分析简化的微分方程。这导致了随机微分方程，我们计划改进现有的非线性随机流行病微分方程的分析方法。使用简化模型，我们然后探讨关键的流行病和经济转型。通过研究渗流阈值和分叉，我们估计的风险达到不希望的状态在不同的层。这一理论框架将铺平道路，以查明耦合范式流行病和经济网络模型的最重要的影响。我们认为，改进的方法，设计，减少，分析和风险估计的多层自适应网络动态可能成为一个基石，有效地管理未来的危机情景。

The dynamics of coupled networks is key to understand many aspects of global crises, in particular, the nature of critical transitions --often associated with collapse-- depends on the coupling of underlying networks. From this viewpoint, the COVID-19 pandemic is not exceptional. The social (epidemic spreading) network, composed of individual humans (agents/nodes) with their social contacts forming the links, is coupled to a number of economic networks through a non-trivial overlap of nodes and links, leading to a large-scale multilayer network. These structures are usually not static but adaptive, as links may emerge or disappear as a result of the dynamics. In this project, we propose to study contact processes as a phenomenon taking place on dynamical adaptive multilayer networks, in particular, coupling epidemic and economic layers. The focus of this interdisciplinary project is on foundational techniques and approaches from network dynamics as employed in theoretical physics and in mathematics that help clarify the nature of critical transitions (collapse or tipping points) in such systems. The first aspect is based on differential equation models where we aim to develop novel ways for moment closure for multilayer networks, which we then test by designing concrete stylized economic-epidemic models. As a second step, we analyze the reduced differential equations by coarse-graining the external multilayer inputs as parametric uncertainty input for a single layer. This leads to stochastic differential equations, where we plan to improve the existing analysis methods for nonlinear stochastic epidemic differential equations. Using reduced models, we then explore critical epidemic and economic transitions. By studying percolation thresholds and bifurcations, we estimate the risk of reaching undesired states in the different layers. This theoretical framework will pave the way to pinpoint the most important effects of coupling paradigmatic epidemic and economic network models. We believe that improved methodology for the design, reduction, analysis, and risk estimation of multilayer adaptive network dynamics could become a cornerstone for an effective management of future crises scenarios.