A research article “Analytical Solutions of the Susceptible-Infected-Virus (SIV) Model” by Emily MacIndoe (’19) has been published in SIAM Undergraduate Research Online Journal. McIndoe’s research was completed as part of her honors requirement in the spring of 2019, and she was advised by Associate Professor of Mathematics Jangwoon “Leo” Lee. “It is highly unusual for a student to publish a paper in mathematics,” said College of Arts and Sciences Dean Keith Mellinger, who praised MacIndoe’s work and wished her “a hearty congratulations.” McIndoe’s paper is accessible through the following link on the Society for Industrial and Applied Mathematics website: https://www.siam.org/Publications/SIURO/Volume-12.
Abstract: The Susceptible-Infected-Virus (SIV) model is a compartmental model to describe within-host dynamics of a viral infection. We apply the SIV model to the human immunodeficiency virus (HIV); in particular, we present analytical solutions to two versions of the model. The first version includes only terms related to the susceptible cell-virus particle interaction and virus production, while the second includes those terms in addition to the infected cell death rate. An analytical solution, although more challenging and time-consuming than numerical methods, has the advantage of giving exact, rather than approximate, results. These results contribute to our understanding of virus dynamics and could be used to develop better treatment options. The approach used to solve each model involved first isolating one of the dependent variables, that is, deriving an equation that involves only one of the variables and its derivatives. Next, various substitutions were used to bring the equation to a more easily solvable form. For the first model, an exact solution is obtained in the form of an implicit equation. For the second model, we give an analytical solution generated by an iterative method.
