AIMS Mathematics, 2020, 5(5): 4136-4150. doi: 10.3934/math.2020265

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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

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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