Spread of Crime Dynamics: A mathematical approach

TL;DR

This paper models the spread of crime in the US using an epidemiological differential equations approach, calculating key metrics and simulating scenarios to inform crime reduction strategies.

Contribution

It introduces a novel epidemiological model with five compartments to analyze crime dynamics, including stability analysis and numerical simulations with real US data.

Findings

Positivity of solutions established

Basic reproduction number calculated

Simulations illustrate factors influencing crime spread

Abstract

In this work, the spread of crime dynamics in the US is analyzed from a mathematical scope, an epidemiological model is established, including five compartments: Susceptible (S), Latent 1 (E1), Latent 2 (E2), Incarcerated (I), and Recovered (R). A system of differential equations is used to model the spread of crime. A result to show the positivity of the solutions for the system is included. The basic reproduction number and the stability for the disease-free equilibrium results are calculated following epidemiological theories. Numerical simulations are performed with US parameter values. Understanding the dynamics of the spread of crime helps to determine what factors may work best together to reduce violent crime.