Stochastic Epidemic-Economic Adaptive Network Dynamics

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.