Mathematical modeling of burglary dynamics incorporating unemployment in Kenya

Abstract

Burglary remains a critical socioeconomic challenge in Kenya, with unemployment identified as a key driver. This study presents a deterministic compartmental model using ordinary differential equations to explore how unemployment influences burglary dynamics in Kenya. The population is divided into five classes: susceptible, exposed, active burglars, incarcerated individuals, and those released from prison. Analytical results demonstrate that the model is well-posed, with positive and bounded solutions. Using the next-generation matrix method, we compute the effective reproduction number R_e to analyze the stability of the burglary-free equilibrium point which is locally and globally asymptomatically stable when R_e < 1 and the burglary-endemic equilibrium point which is both locally and globally asymptotically stable when R_e > 1, indicating persistent burglary. The sensitivity analysis reveals that the employment rate ω is the most critical parameter for control, with a higher employment rate that significantly reduces R_e. Numerical simulations using ODE-45 in MATLAB software corroborate these findings, showing that increased job opportunities drastically lower the incidence of burglary. This study provides insights for policy formulation, highlighting employment creation as an effective strategy to reduce burglary. This work contributes to social mathematical modeling by bridging socioeconomic factors with crime dynamics, offering a replicable framework for similar contexts. The model introduces novel elements such as recidivism and unemployment-linked transmission dynamics, offering a unique contribution to crime modeling in Kenya.