Periodic solutions of a model for tumor virotherapy

Discrete and Continuous Dynamical Systems - Series S

Volumn 4, Issue 6, 2011, Pages 1587-1597

  Vasiliu, Daniel ^a   Tian, Jianjun Paul ^b  

^a CHRISTOPHER NEWPORT UNIVERSITY   (United States)

^b Dept of Economics and Thomas Jefferson Program in Public Policy at the College of William and Mary   (United States)

Author keywords

Hopf bifurcation; Periodic solutions; Tumor model; Virotherapy

Indexed keywords

EID: 79958235798     PISSN: 19371632     EISSN: 19371179     Source Type: Journal    
DOI: 10.3934/dcdss.2011.4.1587     Document Type: Conference Paper

References (11)

1. E. Antonio Chiocca, Oncolytic viruses, Nature reviews, Cancer, 2(2002), 938-950. (Pubitemid 37328895)
2. K. Ikeda, T. Ichikawa, H. Wakimoto, J. S. Silver, D. Finkestein, G. R. Harsh, D. N. Louis, R. T. Bartus, F. H. Hochberg and E. A. Chiocca, Oncolytic virus therapy of multiple tumors in the brain requires suppression of innate and elicited antiviral responses, Nature Med., 5(1999), 881-888.
3. G. Fulci, et al, Cyclophosphamide enhances glioma virotherapy by inhibiting innate immune responses, PNAS Proceedings of the National Academy of Sciences of the United States of America, 103(2006), 12873-12878. (Pubitemid 44298654)
4. H. Kambara, H. Okano, E. A. Chiocca and Y. Saeki, An oncolytic HSV-1 mutant expressing ICP34.5 under control of a nestin promoter increases survival of animals even when symptomatic from a brain tumor, Cancer Research, 65(2005), 2832-2839. (Pubitemid 40490086)
5. H. Kambara, Y. Saeki and E. A Chiocca, Cyclophosphamide allows for in vivo dose reduction of a potent oncolytic virus, Cancer Research, 65(2005), 11255-11258. (Pubitemid 41821678)
6. Shangbin Cui and Avner Friedman, A hyperbolic free boundary problem modeling tumor growth, Interfaces and Free Boundaries, 5(2003), 159-181
7. Avner Friedman, Jianjun Paul Tian, Giulia Fulci, Antonio Chioca and Jin Wang, Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Cancer Research, 4(2006), 2314-2319.
8. Jianjun Paul Tian, Finite-time perturbations of dynamical systems and applications to tumor therapy, appear to Discrete and Continuous Dynamical Systems - B.
9. Peter J. Olver, "Classical Invariant Theory", London Mathematical Society Student Texts, 1999.
10. Lawrence Perko, "Differential Equations and Dynamical Systems", Third Edition, Springer, 2007.
11. D. Roose and V. Hlavaček, A direct method for the computation of Hopf bifurcation points, SIAM Journal of Applied Mathematics, 45(1985), 879-894. (Pubitemid 15601281)