Mathematical Assessment of Methamphetamine Abuse in a Specific Population

Faculty #39
Discipline: Mathematics and Statistics
Subcategory: STEM Research

Aprillya Lanz - Norfolk State University
Co-Author(s): A. B. Gummel, Arizona State University

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Methamphetamine is an addictive stimulant that releases high levels of neurotransmitter dopamine. The use of methamphetamine has shown to increase libido and reduces inhibition. As a result, methamphetamine is commonly used among men who have sex with men to initiate, enhance, and prolong sexual encounters. This, in turns, promotes high risk sexual behavior in this community of methamphetamine users which increases the risk of acquiring an STD. Furthermore, studies have shown that the use of methamphetamine is associated with more frequent risky sexual behaviors among HIV positive men when compared with HIV negative men. In this poster, we will present a compartmental model that represents the dynamics of methamphetamine abuse and HIV transmission in the men seeking men community from a mathematical perspective. The model considers different stages of progression of meth use and individuals who are temporary or permanently quitters. The analysis of the model reveals that the meth-free equilibrium is globally-asymptotically stable whenever the meth-generation number, a threshold value, is less than unity, and unstable if this value is greater than unity. Simulations of the model using a reasonable set of parameter values will be presented to represent different possible scenarios.

Funder Acknowledgement(s): NSF HBCU-UP Grant No. 1505498

Faculty Advisor: None Listed,