Mathematical Modelling in Criminology

This paper, determines the possible position of the serial criminals by solving the geographical outline problem using our developed mathematical model. Under a series of reasonable assumption, we build some models for different types of cases, including the optimization model with the minimal distance, the GM (1, 1) model, the probability contour model and the escape model. We use two schemes to generate two geographical profiles, and then give an efficient prediction by combining them together. The predictions contain the locations where the murderer is most likely to live with its approximate range and the possible time of the next crime. Furthermore, the degree of confidence of the prediction is also given. In addition, we give an executive summery which introduces our technique briefly and provide a broad overview of the potential issue. Applying the optimization model with the minimal impact, we firstly determine the geographical profile where the criminal may hide. Moreover, we estimate the next crime time with the GM (1,1) model. Then we use the probability contour model to predict the profile of the next possible crime locations. Taking this all into consideration, we give a useful and efficient scheme and test it for some cases. Also, we built an escape model for the situation in which the murderer still commits crimes in escape. Finally, a summary is made, in which we provide suitable and unsuitable cases for each model. Besides, the strengths and weaknesses of the model as well as the possible way to improve the models are discussed.