Accession Number : AD1013474


Title :   Mathematical Modeling: Immune System Dynamics in the Presence of Cancer and Immunodeficiency in vivo


Descriptive Note : Technical Report


Corporate Author : U.S. Naval Academy Annapolis United States


Personal Author(s) : Wester,Thomas J


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/1013474.pdf


Report Date : 11 May 2016


Pagination or Media Count : 136


Abstract : 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.


Descriptors :   Human immunodeficiency viruses , Mathematical models , cancer , IMMUNE SYSTEM , Nonlinear differential equations , hiv infections , mathematical analysis , infection , neoplasms , stability


Distribution Statement : APPROVED FOR PUBLIC RELEASE