Faculty Mentor

Dr. Kristen Abernathy & Dr. Zach Abernathy


College of Arts and Sciences


Department of Mathematics



Download Poster (427 KB)


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.

Publication Date





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

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

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.