School of Mathematical & Statistical Sciences Faculty Publications

Mathematical Modeling of Methamphetamine Market Dynamics: Insights into User-Gang-Cartel Interactions and Policy Implications

Document Type

Article

Publication Date

4-2026

Abstract

Using compartmental models, we study the complex dynamics of a hypothetical methamphetamine trafficking market. Analyzing the basic reproductive number for Model I, we see that reducing gang-susceptible interaction or increasing gang arrests can decrease drug prevalence. Model II considers drug initiation, finding that cartels can maintain market dominance and sustained growth, particularly when regulations inhibit local gangs from producing methamphetamine. Showing that higher drug purity and affordability result in fewer vulnerable people and more gang and cartel members. Model III reformulates the interaction, showing that a fraction of gang members may transition to cartels. Our modeling shows the methamphetamine crisis may be better addressed by reducing demand rather than limiting supply, which also helps understand how drug availability, quality, and price relate to use, abuse, and social issues.

Comments

© 2026 The Author(s), under exclusive license to Springer Nature Switzerland AG.

https://rdcu.be/flu1V

Publication Title

Analysis and PDE in Developing Countries

DOI

10.1007/978-3-032-14211-5_15

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