Modeling the impact of civilian firearm ownership in the evolution of violent crimes

TL;DR

This paper introduces a mathematical model using differential equations to analyze how civilian firearm ownership influences the evolution of violent crimes, highlighting that increased legal gun access correlates with higher crime rates.

Contribution

The study presents a novel differential equations model incorporating legal and illegal guns to understand violent crime dynamics, providing analytical and numerical insights.

Findings

Legal gun increase accelerates violent crimes

Illegal guns contribute to rising criminality

Model suggests firearm access impacts crime control

Abstract

We propose a simple mathematical model to describe the evolution of violent crimes. For such purpose, we built a model based on ordinary differential equations that take into account the number of violent crimes and the number of legal and illegal guns. The dynamics is governed by probabilities, modeling for example the police action, the risk perception regarding crimes that leads to increase of ownership of legal guns, and so on. Our analytical and numerical results show that, in addition to the rise of criminality due to the presence of illegal guns, the increase of legal guns leads to a fast increase of violent crimes, suggesting that the access of firearms by civilians is not a good option regarding the control of crimes.