International Conference on Applications of Mathematics to Nonlinear Sciences. Electron. J. Diff. Eqns., Conference 24 (2017), pp. 23-33.

A mechanism by which mass incarceration contributes to HIV disparities in the United States

David J. Gerberry, Hem Raj Joshi

Abstract:
In this work, we develop a mathematical model of HIV epidemiology to explore a possible mechanism by which mass incarceration can lead to increased HIV incidence. The results are particularly relevant for the African American community in the United States that represents only 12& of the total population but accounts for 45& of HIV diagnoses and 40& of the incarcerated population. While most explanations of the link between mass incarceration (or anything else that leads to a population with a low ratio of males to females) and higher HIV burden are based on the complicated idea of sexual concurrency, we propose a much simpler mechanism based on the idea of sexual activity compensation.
The primary assumption behind this mechanism is that females determine the overall level of sexual activity in a population. Consequently, sexual activity will remain relatively stable even when male-to-female ratios are low.
For this to be possible, the pool of men will increase their sexual activity to meet the demands of the female population. Through mathematical analysis and numerical simulation, we demonstrate that these assumptions produce a situation in which mass incarceration (and low male-to-female ratios, in general) lead to higher HIV incidence.

Published November 15, 2017.
Math Subject Classifications: 35K28, 34R60, 92B99.
Key Words: HIV epidemiology; mass incarceration and HIV incidence; male-female ratio; R0.

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David J. Gerberry
Department of Mathematics
Xavier University
Cincinnati, Ohio 45207, USA
email: david.gerberry@xavier.edu
Hem Raj Joshi
Department of Mathematics
Xavier University
Cincinnati, Ohio 45207, USA
email: joshi@xavier.edu

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