Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Periodic solutions of a model for tumor virotherapy

Pages: 1587 - 1597, Volume 4, Issue 6, December 2011      doi:10.3934/dcdss.2011.4.1587

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Daniel Vasiliu - Department of Mathematics, Christopher Newport University, Newport News VA, 23606, United States (email)
Jianjun Paul Tian - Mathematics Department, College of William and Mary, Williamsburg, VA 23187, United States (email)

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:  Periodic solutions, Hopf bifurcation, virotherapy, tumor model.
Mathematics Subject Classification:  Primary: 92C37; Secondary: 34A34.

Received: April 2009;      Revised: October 2009;      Available Online: December 2010.