Spread of Crime Dynamics: A Mathematical Approach

In this work, the spread of crime dynamics in the US is analyzed from a mathematical perspective. An epidemiological model is established, including five compartments: Susceptible ($S$), Latent 1 ($E_1$), Latent 2 ($E_2)$, Incarcerated ($I$), and Recovered ($R$). A system of differential equations is used to model the spread of crime. A result demonstrating the positivity of the solutions for the system is included. The basic reproduction number and the stability of the disease-free equilibrium are calculated following epidemiological theories. Numerical simulations are performed with US-specific parameter values. Understanding the dynamics of the spread of crime helps to determine what factors may work best to reduce violent crime effectively.