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
  1. I. AthanassiosD. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comp. Biomedical Res., 33 (2000), 211–226. [CrossRef] [PubMed]
  2. 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.
  3. P. C. Das, R. R. Sharma. On optimal controls for measure delay-differential equations. SIAM J. Control, 6 (1971) No. 1, 43–61. [CrossRef]
  4. 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]
  5. 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. [CrossRef] [MathSciNet]
  6. 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.
  7. R. D. Driver. Ordinary and Delay Differential Equations. Springer-Verlag, New York, 285–311, 1977.
  8. K. R. Fister, J. H. Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences in Engineering, 2 (2005), No. 3, 499–510.
  9. R. Fletcher. Practical methods of optimization. Wiley and Sons, New York, 1987.
  10. 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.
  11. 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. [CrossRef] [PubMed]
  12. D. KirschnerJ. C. Panetta. Modeling immunotherapy of the tumor-immune interaction. Journal of Mathematical Biology, 35 (1998), 235–252.
  13. 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]
  14. D. McKenzie. Mathematical modeling and cancer. SIAM News, 31, Jan/Feb 2004.
  15. J. M. Murray. Some optimality control problems in cancer chemotherapy with a toxicity limit. Mathematical Biosciences, 100 (1990), 49–67. [CrossRef] [MathSciNet] [PubMed]
  16. L. S. Pontryagin, V. G. Boltyanksii, R. V. Gamkrelidze, E. F. Mischchenko. The Mathematical theory of optimal processes. Wiley, New York, 1962.
  17. G. W. Swan, T. L. Vincent. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bulletin of Mathematical Biology, 39 (1977), 317–337. [PubMed]
  18. M. Villasana, A. Radunskaya. A delay differential equation model for tumor growth. Journal of Mathematical Biology, 47 (2003), 270–294. [CrossRef] [MathSciNet] [PubMed]

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