A comparison of heroin epidemic models

TL;DR

This paper compares two mathematical models of heroin use in communities, analyzing their stability and implications for eradication or endemic persistence of heroin addiction.

Contribution

It introduces a new heroin epidemic model and compares its stability properties with an existing model, providing insights into long-term outcomes.

Findings

Both models exhibit stable equilibria indicating possible eradication or endemic states.

The new model's stability analysis aligns with the existing model, validating its relevance.

Implications for policy and intervention strategies are discussed based on model outcomes.

Abstract

The use of illicit drugs has been on the rise in United States. It is very detrimental on society, as fatal overdose is the fourth leading cause of death in the United States, which is about the same as motor vehicle crashes. Of all illicit drugs, one drug that has an severe adverse effect on a community as a whole is heroin. This paper will discuss two mathematical models- the White and Comiskey model and a newly introduced model proposed by the author, describing heroin use within a fixed community. We will show the existence of stable equilibrium from both models, suggesting both a situation where heroin use is eradicated and one where it remains an endemic.