Spatial modeling of crime dynamics: Patch and reaction–diffusion compartmental systems

Author:

Calatayud Julia1ORCID,Jornet Marc2ORCID,Mateu Jorge1ORCID

Affiliation:

1. Departament de Matemàtiques Universitat Jaume I Castellón 12071 Spain

2. Departament de Matemàtiques Universitat de València Burjassot 46100 Spain

Abstract

We study the dynamics of abstract models for crime evolution. The population is divided into three compartments, taking into account the participation in crime and incarceration. Individuals transit between the three segments, assuming that having more contact with criminally active people increases one's risk of learning and acquiring the same traits; essentially, crime is regarded as a social epidemic. In the literature, there are several models of this type, based on spatial homogeneity and ordinary differential equations. However, these ideas have not been extended to account for spatial variability. Here, we achieve this target with discrete and continuous forms of space: patch and reaction–diffusion compartmental systems, respectively. We build the models and focus on the effect of the basic reproduction number on the long‐term dynamics of crime (persistence or disappearance). Several theoretical results are presented, which are supported by numerical simulations.

Funder

Generalitat Valenciana

Ministerio de Ciencia e Innovación

Universitat Jaume I

Publisher

Wiley

Subject

General Engineering,General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Reaction-diffusion models of crimo–taxis in a street;Applied Mathematics and Computation;2024-04

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