This project develops and uses mathematical models and computational methods to study human immunodeficiency virus (HIV) infection dynamics under conditioning of drugs of abuse. Drug-addicted HIV patients often suffer from enhanced HIV-associated pathogenic consequences, such as reduced host defenses against infection and development of HIV-associated neurocognitive disorders (HAND). Despite being a critical problem for both science and society, the HIV infection dynamics in the context of drug abuse currently remains one of the least understood areas of HIV biology. In the absence of such knowledge, the ability to devise effective strategies to properly manage the virus infection under drug-abuse conditioning remains one of the biggest challenging efforts. In this project, mathematical and computational models are developed to study HIV dynamics in the circulation and in the brain under drug-abuse conditioning, such as the presence of morphine within the host. Further complex models are developed to study the effects of pharmacodynamic properties of morphine on HIV infection in the circulation and in the brain. The developed models are also used for formulating optimal control problems in order to identify ideal antiretroviral treatment as pre-exposure prophylaxis for HIV-infected drug abusers. In addition to improving our current knowledge of HIV dynamics, pathogenesis and development of HAND under conditioning of drugs of abuse, this research endures a significant positive and practical impact on developing therapies and vaccines to control the burden of HIV among drug abusers.
This project produces autonomous models of the HIV dynamics under conditioning of drugs of abuse in the circulation and in the brain, as well as nonautonomous models incorporating the effects of pharmacodynamic properties of drugs of abuse on HIV infection dynamics. The models are parameterized using experimental data from simian immunodeficiency virus (SIV) infections of morphine-addicted macaques (animal model of HIV). The developed models are extensively analyzed using the tools of mathematical modeling, dynamical systems theory, bifurcation theory, asymptotic analysis, theory of periodic systems, stability and persistence theory, as well as statistical and numerical methods. Mathematical challenges anticipated in this research offer opportunities to develop new mathematical theories that advance the field of applied differential equations and optimal control theory. Results, including optimal antiretroviral therapy treatment protocols, help healthcare professionals to mitigate burdens from HIV infection and HAND in drug abusers, thereby, providing the quality of life to drug-addicted HIV infected patients and their families. In addition, this project provides extensive interdisciplinary collaborative research training opportunities for undergraduate and graduate students from mathematics and biology departments, as well as the School of Pharmacy at University of Missouri-Kansas City (UMKC). The research opportunities will be especially extended to a variety of undergraduate research programs that place priority on involving underrepresented students, particularly, undergraduate rural students from Missouri and Kansas. The research will be incorporated into an interdisciplinary mathematical biology course, cross-listed between graduate and undergraduate levels.
