Free Access
| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010
Mathematical modeling in the medical sciences
|
|
|---|---|---|
| Page(s) | 63 - 75 | |
| DOI | https://doi.org/10.1051/mmnp/20105305 | |
| Published online | 28 April 2010 | |
- I. AthanassiosD. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comp. Biomedical Res., 33 (2000), 211–226. [Google Scholar]
- M. Chaplain, A. Matzavinos. Mathematical modelling of spatio-temporal phenomena in tumour immunology. Tutorials in Mathematical Biosciences III; Cell Cycle, Proliferation, and Cancer, 131–183, Springer-Verlag, Berlin, 2006. [Google Scholar]
- P. C. Das, R. R. Sharma. On optimal controls for measure delay-differential equations. SIAM J. Control, 6 (1971) No. 1, 43–61. [CrossRef] [Google Scholar]
- L. G. de Pillis, K. R. Fister, W. Gu, T. Head, K. Maples, A. Murugan, T. Neal, K. Kozai. Optimal control of mixed immunotherapy and chemotherapy of tumors. Journal of Biological Systems, 16 (2008), No. 1, 51–80. [CrossRef] [Google Scholar]
- L.G. de Pillis, K. R. Fister, W. Gu, C. Collins, M. Daub, D. Gross, J. MooreB. Preskill. Mathematical Model Creation for Cancer Chemo-Immunotherapy. Computational and Mathematical Methods in Medicine, 10 (2009), No. 3, 165–184. [Google Scholar]
- L. G. de Pillis, K. R. Fister, W. Gu, C. Collins, M. Daub, D. Gross, J. Moore, B. Preskill. Seeking Bang-Bang Solutions of Mixed Immuno-chemotherapy of tumors. Electronic Journal of Differential Equations, (2007), No. 171, 1–24. [Google Scholar]
- R. D. Driver. Ordinary and Delay Differential Equations. Springer-Verlag, New York, 285–311, 1977. [Google Scholar]
- K. R. Fister, J. H. Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences in Engineering, 2 (2005), No. 3, 499–510. [Google Scholar]
- R. Fletcher. Practical methods of optimization. Wiley and Sons, New York, 1987. [Google Scholar]
- M. I. Kamien, N. L. Schwartz. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management, Vol. 31 of Advanced Textbooks in Economics. North-Holland, 2nd edition, 1991. [Google Scholar]
- M. Kim, S. Perry, and K. B. Woo. Quantitative approach to the deisgn of antitumor drug dosage schedule via cell cycle kinetics and systems theory. Ann. Biomed. Eng., 5 (1977), 12–33. [Google Scholar]
- D. KirschnerJ. C. Panetta. Modeling immunotherapy of the tumor-immune interaction. Journal of Mathematical Biology, 35 (1998), 235–252. [Google Scholar]
- W. Liu, T. Hillen, H. I. Freedman. A Mathematical model for M-phase specific chemotherapy including the Go-phase and immunoresponse. Mathematical Biosciences and Engineering, 4 (2007), No. 2, 239-259. [MathSciNet] [Google Scholar]
- D. McKenzie. Mathematical modeling and cancer. SIAM News, 31, Jan/Feb 2004. [Google Scholar]
- J. M. Murray. Some optimality control problems in cancer chemotherapy with a toxicity limit. Mathematical Biosciences, 100 (1990), 49–67. [Google Scholar]
- L. S. Pontryagin, V. G. Boltyanksii, R. V. Gamkrelidze, E. F. Mischchenko. The Mathematical theory of optimal processes. Wiley, New York, 1962. [Google Scholar]
- G. W. Swan, T. L. Vincent. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bulletin of Mathematical Biology, 39 (1977), 317–337. [Google Scholar]
- M. Villasana, A. Radunskaya. A delay differential equation model for tumor growth. Journal of Mathematical Biology, 47 (2003), 270–294. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.