共享资源下的网络多病毒传播分析与防范策略
Networked Multi-Virus Spread with a Shared Resource: Analysis and Mitigation Strategies
摘要：
研究了具有共享资源的多竞争连续时间传染病过程。我们考虑的设置中，多种病毒同时流行的人群，传播发生，不仅由于个人与个人的相互作用，但也由于个人与资源的相互作用。在这种情况下，一个人要么不受任何病毒的影响，要么被多种病毒中的一种感染。我们将平衡分为三类：a）健康状态（所有病毒都被根除），b）单病毒流行平衡（除了一种病毒之外，所有病毒都被根除），c）共存平衡（多种病毒同时感染不同的人群）。我们提供i）指数（分别）的一个充分条件。渐近）根除病毒; ii）单病毒流行平衡的存在性、唯一性和渐近稳定性的充分条件; iii）健康状态是唯一平衡的充要条件;以及iv）对于双病毒设置（即，两个竞争的病毒），共存平衡存在的充分条件和必要条件。基于这些分析结果，我们提供了两种缓解策略：一种技术，保证收敛到健康的状态;和，在双病毒设置，一个计划，采用一种病毒，以确保其他病毒被根除。结果表明，在斯德哥尔摩市的蔓延情况下的数值研究。
英文摘要：
The paper studies multi-competitive continuous-time epidemic processes in the presence of a shared resource. We consider the setting where multiple viruses are simultaneously prevalent in the population, and the spread occurs due to not only individual-to-individual interaction but also due to individual-to-resource interaction. In such a setting, an individual is either not affected by any of the viruses, or infected by one and exactly one of the multiple viruses. We classify the equilibria into three classes: a) the healthy state (all viruses are eradicated), b) single-virus endemic equilibria (all but one viruses are eradicated), and c) coexisting equilibria (multiple viruses simultaneously infect separate fractions of the population). We provide i) a sufficient condition for exponential (resp. asymptotic) eradication of a virus; ii) a sufficient condition for the existence, uniqueness and asymptotic stability of a single-virus endemic equilibrium; iii) a necessary and sufficient condition for the healthy state to be the unique equilibrium; and iv) for the bi-virus setting (i.e., two competing viruses), a sufficient condition and a necessary condition for the existence of a coexisting equilibrium. Building on these analytical results, we provide two mitigation strategies: a technique that guarantees convergence to the healthy state; and, in a bi-virus setup, a scheme that employs one virus to ensure that the other virus is eradicated. The results are illustrated in a numerical study of a spread scenario in Stockholm city.
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