A mathematical model for tumor growth and treatment using virotherapy

Zachary Abernathy; Kristen Abernathy; Jessica Stevens; Zachary Abernathy; Kristen Abernathy; Jessica Stevens

doi:10.3934/math.2020265

AIMS Mathematics

2020, Volume 5, Issue 5: 4136-4150. doi: 10.3934/math.2020265

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Research article

A mathematical model for tumor growth and treatment using virotherapy

1.
Department of Mathematics, Winthrop University, 701 Oakland Ave., Rock Hill, SC 29733, USA
2.
Department of Mathematics, North Carolina State University, 2108 SAS Hall, Raleigh, NC 27695

Received: 10 February 2020 Accepted: 14 April 2020 Published: 28 April 2020
MSC : 34D23

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.
- cancer,
- virotherapy,
- global stability,
- long-term dynamics
Citation: Zachary Abernathy, Kristen Abernathy, Jessica Stevens. A mathematical model for tumor growth and treatment using virotherapy[J]. AIMS Mathematics, 2020, 5(5): 4136-4150. doi: 10.3934/math.2020265

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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. 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.

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