`a`
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Treatment of glioma with virotherapy and TNF-$\alpha$ inhibitors: Analysis as a dynamical system
Pages: 425 - 441, Issue 1, January 2018

doi:10.3934/dcdsb.2018029      Abstract        References        Full text (1034.4K)           Related Articles

Elzbieta Ratajczyk - Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland (email)
Urszula Ledzewicz - Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653, United States (email)
Maciej Leszczyński - Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, Poland (email)
Heinz Schättler - Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo 63130, United States (email)

1 A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge University Press, Cambridge, 1993.       
2 B. Auffinger, A. U. Ahmed and M. S. Lesniak, Oncolytic virotherapy for malignant glioma: Translating laboratory insights into clinical practice, Front. Oncol., 3 (2013).
3 Z. Bajzer, T. Carr, K. Josić, S. J. Russell and D. Dingli, Modeling of cancer virotherapy with recombinant viruses, J. Theoretical Biology, 252 (2008), 109-122.       
4 M. Biesecker, J. H. Kimn, H. Lu, D. Dingli and Z. Bajzer, Optimization of virotherapy for cancer, Bull. Math. Biology, 72 (2010), 469-489.       
5 E. A. Chiocca, Oncolytic viruses, Nat. Rev. Cancer, 2 (2002), 938-950.
6 B. S. Choudhury and B. Nasipuri, Efficient virotherapy of cancer in the presence of immune response, Int. J. Dynamics and Control, 2 (2014), 314-325.
7 J. J. Crivelli, J. Földes, P. S. Kim and J. Wares, A mathematical model for cell-cycle specific cancer virotherapy, J. of Biological Dynamics, 6 (2012), 104-120.       
8 A. El-alami Laaroussi, M. El Hia, M. Rachik, E. Benlahmar and Z. Rachik, Analysis of a mathematical model for treatment of cancer with oncolytic virotherapy, Appl. Math. Sci., 8 (2014), 929-940.
9 A. Friedman, J. Tian, G. Fulci, E. Chioca, J. Wang, Glioma virotherapy: Effects of innate immune suppression and increased viral replication capacity, Can. Res., 66 (2006), 2314-2319.
10 G. Fulci, L. Breymann, D. Gianni, K. Kurozomi, S. S. Rhee, J. Yu, B. Kaur, D. N. Louis, R. Weissleder, M. A. Caligiuri and E. A. Chiocca, Cyclophosphamide enhances glioma virotherapy by inhibiting innate immune responses, Proc. of the National Academy of Sciences - PNAS, 103 (2006), 12873-12878.
11 J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Verlag, New York, 1983.       
12 N. L. Komarova and D. Wodarz, Targeted Cancer Treatment in Silico - Small Molecule inhibitors and Oncolytic Viruses, Birkhäuser, 2014.       
13 L. R. Paiva, C. Binny, S. C. Ferreira jr. and M. L. Martins, A multiscale mathematical model for oncolytic virotherapy, Can. Res., 69 (2009), 1205-1211.
14 E. Ratajczyk, U. Ledzewicz, M. Leszczyński and A. Friedman, The role of TNF-$\alpha$ Inhibitor in Glioma virotherapy: A mathematical model, Math. Biosci. and Engr. - MBE, 14 (2017), 305-319.       
15 D. Wodarz, Viruses as antitumor weapons: Defining conditions for tumor remission, Can. Res., 61 (2001), 3501-3507.

Go to top