# Modelling the Effects of Complacency and Educational Countermeasures on the Spread of HIV

## Faculty Mentor

Two WU mentors: Zach Abernathy, Ph.D.; Kristen Abernathy, Ph.D.; abernathyz@winthrop.edu; abernathyk@winthrop.edu

## College

College of Arts and Sciences

Mathematics

## Faculty Mentor

Zach Abernathy, Ph.D.; Kristen Abernathy, Ph.D.

## Abstract

In this project, we consider a system of five ordinary differential equations which describe the population dynamics of HIV/AIDS when individuals are tested for the virus and then moved onto antiretroviral therapy. We include a Holling Type-II response to model the complacency of the population in response to the number of AIDS cases. We prove global stability of the disease-free equilibrium when the basic reproductive ratio is less than one. We then derive an optimal control problem and solve it theoretically using Pontryagin's Maximum Principle and numerically using the Forward-Backward Sweep Method. We conclude with a discussion on the impact of optimal educational strategies to combat complacency regarding the AIDS/HIV epidemic.

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## Grant Support

This project was supported by SC INBRE grants from the National Institute of General Medical Sciences (2P20 GM10349915) of the National Institutes of Health.

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Modelling the Effects of Complacency and Educational Countermeasures on the Spread of HIV

In this project, we consider a system of five ordinary differential equations which describe the population dynamics of HIV/AIDS when individuals are tested for the virus and then moved onto antiretroviral therapy. We include a Holling Type-II response to model the complacency of the population in response to the number of AIDS cases. We prove global stability of the disease-free equilibrium when the basic reproductive ratio is less than one. We then derive an optimal control problem and solve it theoretically using Pontryagin's Maximum Principle and numerically using the Forward-Backward Sweep Method. We conclude with a discussion on the impact of optimal educational strategies to combat complacency regarding the AIDS/HIV epidemic.