Mathematical models for predicting the geographical distribution of areas with high rates of home burglary and numerical experiments to evaluate the effectiveness of police patrol routing strategies in reducing crime can support security policymakers in planning more effective patrol routes. We give an overview of the model formulated by Jones et al. (2010) to study the effects of the presence of law enforcement on the formation of home-burglary hotspots. We propose an extension of the model to contemplate that a small proportion of burglars travel far away from their awareness space to burgle houses. We incorporate these trips in the form of long-range stochastic jumps that are biased towards more attractive sites. Simulations suggest that hotspots lose attractiveness as police more influences via deterrence on burglars’ decision making about returning home rather than burglarizing a house. The results indicate that a higher proportion of burglars making long crime journeys might counteract the deterrent effect form the police presence. A case study is carried out to predict at the zone and citywide levels the distribution of areas with the highest home burglary rates in Mexico City. The L-BFGS method is applied to get the values for the parameters in both the Jones et al. model and our model; we use data from home burglaries reported, patrol zones and prison admissions. The minimum of the objective function is slightly lower for our model than for the Jones et al. model. Results obtained through numerical simulations using our model better fit the spatial statistical distribution of home-burglary hotspots for the entire city than for the zones.

用于预测家庭盗窃发生率较高的地区的地理分布的数学模型，以及用于评估警察巡逻路线策略在减少犯罪方面的有效性的数值实验，可以支持安全政策制定者规划更有效的巡逻路线。我们对Jones等人提出的模型进行了概述。（2010）研究存在的执法对家庭入室盗窃热点形成的影响。我们建议对该模型进行扩展，以考虑到一小部分窃贼从其认知空间转移到窃贼房屋。我们将这些旅行以远程随机跳跃的形式纳入其中，这些旅行倾向于偏向更具吸引力的网站。模拟结果表明，随着警察更多地通过威慑手段来防止小偷对回家的决定而不是对房子进行防盗，热点地区失去了吸引力。结果表明，进行长途犯罪的盗贼比例较高，可能会抵消警察在场的威慑作用。进行了一个案例研究，以预测该地区和全市级别家庭盗窃率最高的地区在墨西哥城的分布。L-BFGS方法用于获得Jones等人的参数值。模型和我们的模型；我们使用报告的家庭盗窃，巡逻区和监狱入场的数据。对于我们的模型，目标函数的最小值略低于Jones等人的模型。模型。