You have no items in your shopping cart.
ABSTRCT
This thesis consists of six chapters. The First Chapter (1) presents an introduction to the study. Crime statistics, classification of crime and criminal justices system were extensively discussed. Additionally, the review of current and relevant mathematical literature that have been used to answer specific sociological issues were presented. This Chapter also contains the motivation and statement of the problem for the study as well as the aim and objectives of the research. In Chapter Two (2), the development of the criminal gang model (ordinary differential equation) based on age-structured paradigm is presented. The Chapter also shows the analysis of the model using tool from non-linear dynamical system theory. The numerical simulation of the model which is to gain insight into the quantitative properties of the model is presented as well. Furthermore, Chapter Three (3) is divided into two different parts. The first part contains a detailed investigation of oscillatory properties of the criminal gang model. The existence of damping and sustained oscillations leading to the existence of limit circle are presented. The second part of the model shows the development, analysis and numerical simulation of the optimal control model with two control functions. Chapter Four (4) pays particular attention to the study of criminal gang model leading to formulation of delay differential equations. The system of delay differential equations consist of three delay terms. The qualitative and quantitative properties were extensively presented and discussed. Chapter Five (5) outlines another criminal gang model based on gang rivalry between two criminal gangs. Also, the qualitative properties and quantitative properties were extensively studied and discussed. Chapter Six (6) deals with the summary, conclusion, future research, findings and contributions to knowledge while the references and the appendix were considered along with my vit
