MATHEMATICAL MODELING OF BURGLARY DYNAMICS INCORPORATING UNEMPLOYMENT IN KENYA

Abstract

Burglary remains a significant concern in Kenya, affecting the country’s economy and social fabric. It is often driven by the perceived presence of valuable commodi ties in targeted premises and has been linked to other crimes such as rape, arson, and others. The key factors contributing to burglary in Kenya include poverty, un employment, corruption in the criminal justice system, peer pressure, drug abuse, and high levels of education, among others. According to the December 2023 report by the National Crime Research Center, unemployment was identified as the leading contributor to burglary incidences. The financial constraints resulting from unemployment increase the likelihood of individuals resorting to burglary as a means of meeting basic needs and financial obligations. Unemployment increases the chances of people turning to burglary due to the lack of a legitimate income source. This study formulated and analyzed a deterministic mathematical model that described the dynamics of burglary as influenced by unemployment in Kenya using ordinary differential equations. The model solution was shown to be pos itive and bounded, confirming its well-posedness. The existence of steady states was analyzed and the effective reproduction number was derived using the next generation matrix approach. The burglary-free equilibrium was proven to be locally and globally asymptotically stable when Re < 1, while the endemic equilibrium was locally and globally asymptotically stable when Re > 1. The sensitivity analysis of Re with respect to the model parameters was carried out using the normalized forward sensitivity index, which showed that the contact rate between susceptible individuals and burglars τ and the rate at which susceptible individuals became burglars upon contact δ were the least sensitive parameters, while the employment rate ω was the most sensitive parameter. The lower the rate of employment in Kenya, the higher the prevalence rate of burglary in the human population. Nu merical simulations of the developed model were performed using ODE 45 solver in MATLAB software, and the results demonstrated that a high employment rate or the creation of job opportunities among youth drastically reduces burglary inci dences. The findings of this study offer valuable information to decision makers in the National Police Service and other security agencies, highlighting critical areas for intervention to curb burglary in Kenya. Furthermore, this work contributes to the broader field of social mathematical modeling by providing a framework for analyzing crime dynamics resulting from socioeconomic factors.