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Periodic solutions of a model for tumor virotherapy
1. | Department of Mathematics, Christopher Newport University, Newport News VA, 23606, United States |
2. | Mathematics Department, College of William and Mary, Williamsburg, VA 23187, United States |
References:
[1] |
E. Antonio Chiocca, Oncolytic viruses, Nature reviews, Cancer, 2 (2002), 938-950.
doi: 10.1038/nrc948. |
[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.
doi: 10.1038/11320. |
[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. |
[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.
doi: 10.1158/0008-5472.CAN-04-3227. |
[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.
doi: 10.1158/0008-5472.CAN-05-2278. |
[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.
doi: 10.1158/0008-5472.CAN-05-2661. |
[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.
doi: 10.1137/0145053. |
show all references
References:
[1] |
E. Antonio Chiocca, Oncolytic viruses, Nature reviews, Cancer, 2 (2002), 938-950.
doi: 10.1038/nrc948. |
[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.
doi: 10.1038/11320. |
[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. |
[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.
doi: 10.1158/0008-5472.CAN-04-3227. |
[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.
doi: 10.1158/0008-5472.CAN-05-2278. |
[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.
doi: 10.1158/0008-5472.CAN-05-2661. |
[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.
doi: 10.1137/0145053. |
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