A mathematical model for tumor growth and treatment using virotherapy

A mathematical model for tumor growth and treatment using virotherapy

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. We establish a necessary and sufficient treatment condition to...

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Main Authors: Zachary Abernathy, Kristen Abernathy, Jessica Stevens
Format: Article
Language:English
Published: AIMS Press 2020-05-01
Series:AIMS Mathematics
Subjects:
cancer
virotherapy
global stability
long-term dynamics
Online Access:https://www.aimspress.com/article/10.3934/math.2020265/fulltext.html
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spelling doaj-1f4d94a5b93c4eedb36ea7f40f4eca7a2020-11-25T03:10:42ZengAIMS PressAIMS Mathematics2473-69882020-05-01554136415010.3934/math.2020265A mathematical model for tumor growth and treatment using virotherapyZachary Abernathy0Kristen Abernathy1Jessica Stevens21 Department of Mathematics, Winthrop University, 701 Oakland Ave., Rock Hill, SC 29733, USA1 Department of Mathematics, Winthrop University, 701 Oakland Ave., Rock Hill, SC 29733, USA2 Department of Mathematics, North Carolina State University, 2108 SAS Hall, Raleigh, NC 27695We 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. We establish a necessary and sufficient treatment condition to ensure a globally stable cure state, and we additionally show the existence of a cancer persistence state when this condition is violated. We provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature, and we conclude with a discussion on the biological implications of our results.https://www.aimspress.com/article/10.3934/math.2020265/fulltext.htmlcancervirotherapyglobal stabilitylong-term dynamics
collection DOAJ
language English
format Article
sources DOAJ
author Zachary Abernathy
Kristen Abernathy
Jessica Stevens
spellingShingle Zachary Abernathy
Kristen Abernathy
Jessica Stevens
A mathematical model for tumor growth and treatment using virotherapy
AIMS Mathematics
cancer
virotherapy
global stability
long-term dynamics
author_facet Zachary Abernathy
Kristen Abernathy
Jessica Stevens
author_sort Zachary Abernathy
title A mathematical model for tumor growth and treatment using virotherapy
title_short A mathematical model for tumor growth and treatment using virotherapy
title_full A mathematical model for tumor growth and treatment using virotherapy
title_fullStr A mathematical model for tumor growth and treatment using virotherapy
title_full_unstemmed A mathematical model for tumor growth and treatment using virotherapy
title_sort mathematical model for tumor growth and treatment using virotherapy
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2020-05-01
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. We establish a necessary and sufficient treatment condition to ensure a globally stable cure state, and we additionally show the existence of a cancer persistence state when this condition is violated. We provide numerical evidence of a Hopf bifurcation under estimated parameter values from the literature, and we conclude with a discussion on the biological implications of our results.
topic cancer
virotherapy
global stability
long-term dynamics
url https://www.aimspress.com/article/10.3934/math.2020265/fulltext.html
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