SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 1303-1331, January 2021.
This article investigates parametric sensitivities of rioting activity, based on a model of the 2005 French riots. Previously validated against a comprehensive data set, the aforementioned modeling efforts were multiscale in nature and applied at the provincial scale for all of France and the municipal scale in the Île-de-France region around Paris. The governing dynamics at the municipal scale include a bandwagon effect, observed in rioting activity wherein an outburst of activity occurs once a “tipping point” threshold is reached in the people engaging in the activity. This tipping point mechanism is modeled using a nonsmooth function, yielding a framework of nonsmooth ODEs, which makes conventional theory and methods unsuitable. In this article, we perform a sensitivity analysis of the municipal-scale model by adopting a recently developed tool in nonsmooth analysis called the lexicographic directional derivative. Numerical solutions are provided from which we can conclude the relative importance of different parameters in the model, in order to discover the underlying mechanisms that play a crucial role in driving the riot activities. It is shown that the exit/removal rate from rioting activity and geographic proximity have the greatest impact on the dynamics of the social contagion. On the other hand, the initial rioting activity and the tipping point seem less influential.

中文翻译：

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使用字典方向微分确定暴乱中的关键参数

SIAM 应用数学杂志，第 81 卷，第 3 期，第 1303-1331 页，2021 年 1 月。
本文基于 2005 年法国骚乱的模型，研究了骚乱活动的参数敏感性。先前针对综合数据集进行了验证，上述建模工作本质上是多尺度的，并应用于全法国的省级尺度和巴黎周围法兰西岛地区的市政尺度。市政规模的治理动态包括在骚乱活动中观察到的跟风效应，其中一旦参与活动的人达到“临界点”阈值，就会爆发活动。这种临界点机制使用非平滑函数建模，产生非平滑 ODE 框架，这使得传统的理论和方法不适用。在本文中，我们通过采用最近开发的非光滑分析工具，称为词典定向导数，对市政尺度模型进行敏感性分析。提供了数值解，从中我们可以得出模型中不同参数的相对重要性，以发现在推动骚乱活动中起关键作用的潜在机制。结果表明，骚乱活动的退出率/撤离率和地理邻近度对社会传染的动态影响最大。另一方面，最初的骚乱活动和临界点似乎影响较小。以发现在推动骚乱活动中起关键作用的潜在机制。结果表明，骚乱活动的退出率/撤离率和地理邻近度对社会传染的动态影响最大。另一方面，最初的骚乱活动和临界点似乎影响较小。以发现在推动骚乱活动中起关键作用的潜在机制。结果表明，骚乱活动的退出率/撤离率和地理邻近度对社会传染的动态影响最大。另一方面，最初的骚乱活动和临界点似乎影响较小。