论文标题
矢量差方程，定义矩阵和多网络的设计，以减少流行病的传播
Vector Difference Equations, Substochastic Matrices, and Design of Multi-Networks to Reduce the Spread of Epidemics
论文作者
论文摘要
长期以来，城市一直是人类发展和进步的成核中心。城市促进了人类创造力和人类疾病的传播，同时，最大程度地减少疾病的传播的努力影响了城市的设计。本文的目的是探索网络上流行病的动态，以帮助设计一个旨在最大程度地降低流行病的未来的多网络城市。为了做到这一点，我们从网络上的SIR模型（易感，感染，删除）开始，该网络代表城市或区域和边缘由区域之间的流量加权。由于目标是稳定零感染稳态，因此我们将离散时间的SIR模型线性化，从而产生每个节点处感染动力学的差异方程，然后包括来自其他节点的感染流动。这产生了感染传播的矢量差方程。然后，我们概括了随机矩阵的概念，以量化此更新方程的动力学。更新矩阵$ m $的条目可能会随着时间而变化，甚至随着节点之间的流量打开和关闭，甚至不连续。这可能会对由代表城市内部和城市之间相互作用的节点之间的弱和强相互作用组成的多网络产生有用的设计约束。
Cities have long served as nucleating centers for human development and advancement. Cities have facilitated the spread of both human creativity and human disease, and at the same time, efforts to minimize the spread of disease have influenced the design of cities. The purpose of this paper is to explore the dynamics of epidemics on networks in order to help design a multi-network city of the future aimed at minimizing the spread of epidemics. In order to do this, we start with the SIR model (susceptible, infected, removed) on a network in which nodes represent cities or regions and edges are weighted by flows between regions. Since the goal is to stabilize the zero infections steady state, we linearize the discrete-time SIR model yielding difference equations for the dynamics of infections at each node and then include flows of infections from other nodes. This yields a vector difference equation for the spread of infections. We then generalize the concept of stochastic matrix in order to quantify the dynamics of this update equation. The entries of the update matrix $M$ may vary in time, even discontinuously as flows between nodes are turned on and off. This may yield useful design constraints for a multi-network composed of weak and strong interactions between pairs of nodes representing interactions within and among cities.
