Periodic solutions of a model for tumor virotherapy

Daniel Vasiliu; Jianjun Paul Tian

doi:10.3934/dcdss.2011.4.1587

Article Contents

2011, Volume 4, Issue 6: 1587-1597. Doi: 10.3934/dcdss.2011.4.1587

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Periodic solutions of a model for tumor virotherapy

Daniel Vasiliu^1, and
Jianjun Paul Tian^2,

1.
Department of Mathematics, Christopher Newport University, Newport News VA, 23606
2.
Mathematics Department, College of William and Mary, Williamsburg, VA 23187

Received: March 31, 2009

Revised: September 30, 2009

Published: November 2011

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Abstract

In this article we study periodic solutions of a mathematical model for brain tumor virotherapy by finding Hopf bifurcations with respect to a biological significant parameter, the burst size of the oncolytic virus. The model is derived from a PDE free boundary problem. Our model is an ODE system with six variables, five of them represent different cell or virus populations, and one represents tumor radius. We prove the existence of Hopf bifurcations, and periodic solutions in a certain interval of the value of the burst size. The evolution of the tumor radius is much influenced by the value of the burst size. We also provide a numerical confirmation.

Keywords:

Mathematics Subject Classification: Primary: 92C37; Secondary: 34A34.

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References

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