### AIMS Mathematics

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

# A mathematical model for tumor growth and treatment using virotherapy

• 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.

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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• 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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