对骚乱、集体行为和流行病的传播进行建模
Modeling the propagation of riots, collective behaviors, and epidemics
摘要：
本文研究了文献[15]中提出的一类反应扩散系统，它推广了流行病学中的SIR型模型。这种系统现在也被用来描述集体行为。在本文中，我们提出了一个建模方法，这些明显不同的现象，通过社会动荡的动态的例子。该模型涉及两个量：社会动荡的水平，或更一般的活动，u和社会紧张的领域v，它们发挥不对称的作用。我们认为u是实际观察到的或明确的量，而v是一个环境的，有时是隐含的，调节u动力学的易感性场。在这篇文章中，我们探讨了这类模型，并证明了几个理论结果的基础上发展的框架[15]，其中目前的工作是一个伴侣文件。我们在这里特别强调两个亚类的系统：张力抑制和张力增强。这些特点分别是对社会紧张局势的负面或正面反馈的动荡。我们建立了这些类的几个属性，并研究了一些扩展。特别是，我们描述了系统的行为后，初始激增的活动。我们表明，该模型可以产生许多不同的定性动态。我们还提供了各种数值模拟来说明我们的结果，并揭示进一步的属性和开放的问题。
英文摘要：
This paper is concerned with a family of Reaction-Diffusion systems that we introduced in [15], and that generalizes the SIR type models from epidemiology. Such systems are now also used to describe collective behaviors.In this paper, we propose a modeling approach for these apparently diverse phenomena through the example of the dynamics of social unrest. The model involves two quantities: the level of social unrest, or more generally activity, u, and a field of social tension v, which play asymmetric roles. We think of u as the actually observed or explicit quantity while v is an ambiant, sometimes implicit, field of susceptibility that modulates the dynamics of u. In this article, we explore this class of model and prove several theoretical results based on the framework developed in [15], of which the present work is a companion paper. We particularly emphasize here two subclasses of systems: tension inhibiting and tension enhancing. These are characterized by respectively a negative or a positivefeedback of the unrest on social tension. We establish several properties for these classes and also study some extensions. In particular, we describe the behavior of the system following an initial surge of activity. We show that the model can give rise to many diverse qualitative dynamics. We also provide a variety of numerical simulations to illustrate our results and to reveal further properties and open questions.
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