DTIC AD1013474: Mathematical Modeling: Immune System Dynamics pdf

DTIC AD1013474: Mathematical Modeling: Immune System Dynamics

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Description of the Book:

The Human Immunodeficiency Virus (HIV) targets CD4 T-cells which are crucial in regulating the immune systems response to foreignpathogens and cancerous cell development. Furthermore, several studies link HIV infection with the proliferation of specific forms ofcancer such as Kaposi Sarcoma and Non-Hodgkins Lymphoma; HIV infected individuals can be several thousand times more likely to bediagnosed with cancer. In this project, we seek to apply systems of nonlinear ordinary differential equations to analyze how the dynamics ofprimary infection affect the proliferation of cancer. We first begin by characterizing the dynamics of HIV infection. During HIV-1 primaryinfection, we know that the virus concentration increases, reaches a peak, and then decreases until it reaches a set point. We studiedlongitudinal data from 18 subjects identified as HIV positive during plasma donation screening and applied several models to analyze thedynamics of the systems and determine the most effective model for characterizing the infection.

We prove existence, uniqueness,positivity, and boundedness, investigate the qualitative behavior of the models, and find the conditions that guarantee the asymptoticstability of the equilibria. In addition, we conduct numerical simulations and sensitivity analyses to illustrate and extend the theoreticalresults. Furthermore, we develop and study a new Tumor-Immunodeficiency model which integrates the effects of an immunodeficiency oncancerous tumor cell development

• Creator/s: Defense Technical Information Center
• Date: 5/11/2016
• Year: 2016
• Book Topics/Themes: DTIC Archive, Wester, Thomas J, U.S. Naval Academy Annapolis United States, Human immunodeficiency viruses, Mathematical models, cancer, IMMUNE SYSTEM, Nonlinear differential equations, hiv infections, mathematical analysis, infection, neoplasms, stability

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