Analysis of Deterministic and Stochastic HIV Models

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