Date

Spring 4-26-2019

Document Type

Honors Project

First Advisor

Lee, Jangwoon

Department Chair or Program Director

Helmstutler, Randall

Degree Name

Bachelor of Science

Major or Concentration

Mathematics

Department or Program

Mathematics

Abstract

In this research paper, I apply the Susceptible-Infected-Virus (SIV) model to the Human Immunodeficiency Virus (HIV). The SIV model is a compartmental model describing within-host dynamics of viral infections; I analyze it in both its deterministic (in which constants are assumed to be known exactly) and stochastic (in which the death rate of the healthy cells is represented by a random variable) forms. First, I give analytical solutions to two simplified versions of the deterministic model. Next, I apply numerical methods to the full deterministic and stochastic systems. The results give an illustrative picture of HIV in-host population dynamics in the absence of treatment. They also demonstrate how randomness can impact the progression of the disease.

Language

English

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