Curtailing crime dynamics: A mathematical approach - Kwofie, Theophilus; Dogbatsey, Matthias; Moore, Stephen E. (Frontiers in Applied Mathematics and Statistics, 2023)
The understanding of crime is critical towards its control and elimination from societies. The cost and effects associated with crime tends to affect the global public-health and socioeconomic development. In this paper, we formulate a mathematical model for studying crime dynamics and incorporating education programs as a tool to assess the population-level impact on the spread of crime. The model is fitted with crime data reported from July, 2021 to June, 2022 by the State of Illinois in The United States (U.S.). By using least squares method, we obtained parameter estimates from the data reported. The model has a global asymptotically stable crime-free equilibrium whenever a certain criminological threshold, known as the effective reproduction number $\mathcal{R}_E$, is less than unity. The global sensitivity analysis is performed primarily to determine the parameters with the most effect on the spread of crime in the State of Illinois. We observe that the community effective contact rate for criminally active individuals ($β_c$), rate of desistance by criminals ($τ$), and the recidivism rate ($ω$) tend to have great impact on the spread of crime. The numerical simulation shows that with an efficacy level of 75% with varying compliance levels $(0%-100%)$, the burden of crime will be reduced drastically. Also, the rate of incarceration has impact on the level of crime, even though to a less effect.