Title of Abstract

A Mathematical Model for Tumor Growth and Treatment Using Virotherapy

Session Title

Cancer and Biomedical Research

College

College of Arts and Sciences

Department

Department of Mathematics

Abstract

We present a system of four nonlinear differential equations to model the use of virotherapy as a treatment for cancer. This model describes interactions among infected tumor cells, uninfected tumor cells, effector T-cells, and virions. Using various stability analysis techniques, we establish a necessary and sufficient treatment condition to ensure a globally stable cure state. We additionally show the existence of a cancer persistence state when this condition is violated and provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature. We conclude with a discussion on the biological implications of our results.

Honors Thesis Committee

Zach Abernathy, Ph.D.; Kristen Abernathy, Ph.D.; and Trent Kull, Ph.D.

Previously Presented/Performed?

SAEOPP McNair/SSS Scholars Research Conference, Atlanta, Georgia, June 2018; Fifth Annual Showcase of Undergraduate Research and Creative Endeavors (SOURCE), Winthrop University, April 2019

Grant Support?

Supported by a Ronald E. McNair Post-Baccalaureate Achievement Program grant from the U.S. Department of Education

Start Date

12-4-2019 1:00 PM

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Apr 12th, 1:00 PM

A Mathematical Model for Tumor Growth and Treatment Using Virotherapy

WEST 219

We present a system of four nonlinear differential equations to model the use of virotherapy as a treatment for cancer. This model describes interactions among infected tumor cells, uninfected tumor cells, effector T-cells, and virions. Using various stability analysis techniques, we establish a necessary and sufficient treatment condition to ensure a globally stable cure state. We additionally show the existence of a cancer persistence state when this condition is violated and provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature. We conclude with a discussion on the biological implications of our results.