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首页> 外文期刊>SIAM journal on applied dynamical systems >An Age-Structured Population Approach for the Mathematical Modeling of Uruail Burglaries
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An Age-Structured Population Approach for the Mathematical Modeling of Uruail Burglaries

机译：乌乌尔盗窃的数学建模的年龄结构性人口方法

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摘要

We propose a nonlinear model for the dynamics of urban burglaries which takes into account the deterring effect of the police. The model focuses on the timing of criminal activity rather than on the spatial spreading of burglaries and it is inspired in the age-dependent population dynamics. The structuring variables are the time elapsed between two consecutive offenses committed by a burglar or suffered by a house. The main ingredients of the model are the propensity of burglars to commit a crime and the rate at which houses are being burgled. These rates are taken as general as possible to allow different scenarios, including the widely used repeat victimization pattern. The dissuasive effect of the active police deployment is introduced by means of a memory term that depends on the number of the last committed burglaries. The asymptotic behavior of the model and the existence of a globally stable equilibrium are determined thanks to a suitable change of variables that involves a continuous rescaling of the time variable. This new approach provides some interesting analytic results on the equilibrium and the expected times between consecutive offenses. Numerical simulations are shown to illustrate these results.
机译：我们为城市盗窃的动态提出了一个非线性模型，以考虑到警察的阻止效应。该模型侧重于犯罪活动的时间，而不是在盗窃的空间传播中，它受到了依赖年龄依赖的人口动态的启发。结构变量是由窃贼犯下或由房子遭受的连续两个连续违法行证经过的时间。该模型的主要成分是盗窃犯罪的倾向，犯罪的倾向和房屋正在爆扣的速度。这些税率尽可能普遍，以允许不同的场景，包括广泛使用的重复受害模式。主动警察部署的劝阻效果是通过记忆术语引入的，这取决于上次承诺的盗窃的数量。由于涉及时间变量的连续重构的变量的合适变量，确定模型的渐近行为和全局稳定平衡的存在。这种新方法提供了一些有趣的分析结果对均衡和连续违法行量之间的预期时间。显示数值模拟来说明这些结果。

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