Event Title

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

Honors Thesis Committee

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

Location

WEST 219

Start Date

12-4-2019 1:00 PM

Description

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.

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

Comments

Jessica is a McNair Scholar

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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.