Date of Award
Spring 4-26-2019
Document Type
Honors Project
Degree Name
Bachelor of Science
Department
Mathematics
Department Chair or Program Director
Helmstutler, Randall
First Advisor
Lee, Jangwoon
Major or Concentration
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.
Recommended Citation
MacIndoe, Emily, "Analysis of Deterministic and Stochastic HIV Models" (2019). Student Research Submissions. 287.
https://scholar.umw.edu/student_research/287