Chaotic behavior in virotherapy for cancer treatment

This paper studies chaotic behavior in cancer dynamics when a treatment procedure is introduced. Recently introduced virotherapy is considered for the cancer treatment. Chaotic behaviors are investigated by using the Lyapunov Exponent for a set of parameters. The chaotic behavior is studied by using the mathematical model of the cancer dynamics involving the virotherapy. Through simulations and the Lyapunov Exponent, it is proven that recently introduced virotherapy exhibits chaotic behavior. The results indicate that virotherapy may result in re-growth of the tumor due to chaotic nature of the treatment.

[1]  L. D. Pillis,et al.  A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth , 2005 .

[2]  Ami Radunskaya,et al.  The dynamics of an optimally controlled tumor model: A case study , 2003 .

[3]  Naser Babaei,et al.  Personalized drug administration for cancer treatment using Model Reference Adaptive Control. , 2015, Journal of theoretical biology.

[4]  J. Bell,et al.  Oncolytic viruses: what's next? , 2007, Current cancer drug targets.

[5]  C. O'Shea,et al.  Viruses – seeking and destroying the tumor program , 2005, Oncogene.

[6]  Awad El-Gohary,et al.  Chaos and optimal control of equilibrium states of tumor system with drug , 2009 .

[7]  A. Hastings Global stability in Lotka-Volterra systems with diffusion , 1978 .

[8]  S. Russell,et al.  History of oncolytic viruses: genesis to genetic engineering. , 2007, Molecular therapy : the journal of the American Society of Gene Therapy.

[9]  D. Kirschner,et al.  Modeling immunotherapy of the tumor – immune interaction , 1998, Journal of mathematical biology.

[10]  Zeljko Bajzer,et al.  Modeling of cancer virotherapy with recombinant measles viruses. , 2008, Journal of theoretical biology.

[11]  S. Russell,et al.  Infected cell carriers: a new strategy for systemic delivery of oncolytic measles viruses in cancer virotherapy. , 2007, Molecular therapy : the journal of the American Society of Gene Therapy.

[12]  Kah-Whye Peng,et al.  Viruses as anticancer drugs. , 2007, Trends in pharmacological sciences.

[13]  Dominik Wodarz,et al.  Gene therapy for killing p53-negative cancer cells: use of replicating versus nonreplicating agents. , 2003, Human gene therapy.

[14]  Jin Wang,et al.  Numerical study for a model of tumor virotherapy , 2008, Applied Mathematics and Computation.

[15]  Stephen P. Banks,et al.  Chaos in a Three-Dimensional Cancer Model , 2010, Int. J. Bifurc. Chaos.