Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
Page(s) 261 - 278
Published online 25 January 2012
  1. I. Athanassios, D. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Compu. 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, (2006), 131–183.
  3. W. Cheney, D. Kincaid. Numerical mathematics and computing. Thomson Brooks/Cole, Belmont, 2008.
  4. C. Collins, K. R. Fister, M. Williams. Optimal control of a cancer cell model with delay. Math. Model. Nat. Phen., 5 (2010), No. 3, 63–71. [CrossRef] [EDP Sciences]
  5. P. C. Das, R. R. Sharma. On optimal controls for measure delay-differential equations. SIAM J. Control, 6 (1971), No. 1, 43–61. [CrossRef]
  6. L. G. dePillis, A. E. Radunskaya. A mathematical tumor model with immune resistance and drug therapy : an optimal control approach. J. Theoretical Medicine, 3 (2001), 79–100. [CrossRef]
  7. L. G. dePillis, A. E. Radunskaya. The dynamics of an optimally controlled tumor model : a case study. Math. Comp. Model., 37 (2003), No. 11, 1221–1244. [CrossRef]
  8. L. G. dePillis, A. E. Radunskaya, C. L. Wiseman. A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Research, 61 (2005), No. 17, 7950–7958.
  9. L. G. dePillis, K. R. Fister, W. Gu, C. Collins, M. Daub, J. Moore, B. Preskill. Mathematical model creation for cancer chemo-immunotherapy. Computational and Math. Methods in Medicine, 10 (2009), No. 3, 165–184. [CrossRef] [MathSciNet]
  10. R. D. Driver. Ordinary and delay differential equations. Springer-Verlag, New York, 1977.
  11. R. Fletcher. Practical methods of optimization. Wiley and Sons, New York, 1987.
  12. W. Lu, T. Hillen, H. I. Freedman. A mathematical model for M-phase specific chemotherapy including the Go-phase and immunoresponse. Math. Biosci. and Engng., 4 (2007), No. 2, 239–259. [CrossRef]
  13. M.I. Kamien, N. L. Schwartz. Dynamic optimization : the calculus of variations and optimal control in economics and management, Advanced Textbooks in Economics. North-Holland, 1991.
  14. M. Kim, S. Perry, K. B. Woo. Quantitative approach to the design of antitumor drug dosage schedule via cell cycle kinetics and systems theory. Ann. Biomed. Engng, 5 (1977), 12–33. [CrossRef] [PubMed]
  15. D. Kirschner, J. C. Panetta. Modeling immunotherapy of the tumor-immune interaction. J. Math. Bio., 35 (1998), 235–252. [CrossRef] [PubMed]
  16. U. Ledzewicz, T. Brown, H. Schattler. Comparison of optimal controls for a model in cancer chemotherapy with l1 and l2 type objectives. Optimization Methods and Software, 19 (2004), No. 3-4, 339–350. [CrossRef] [MathSciNet]
  17. U. Ledzewicz, H. Schattler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete and Continuous Dynamical Systems - Series B, 6 (2006), No. 1, 129–150. [MathSciNet]
  18. D. McKenzie. Mathematical modeling and cancer. SIAM News, 31 (2004), 1–2.
  19. J. M. Murray. Some optimality control problems in cancer chemotherapy with a toxicity limit. Math. Biosci., 100 (1990), 49–67. [CrossRef] [MathSciNet] [PubMed]
  20. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko. The mathematical theory of optimal processes. Gordon and Breach, 1962.
  21. G. W. Swan, T. L. Vincent. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bull. of Math. Bio., 39 (1977), 317–337.
  22. A. Swierniak, U. Ledzewicz, H. Schattler. Optimal control for a class of compartmental models in cancer chemotherapy. Int. J. Appl. Math. Comput. Sci., 13 (2003), No. 3, 357–368. [MathSciNet]
  23. M. Villasana A. Radunskaya. A delay differential equation model for tumor growth. J. Math. Bio., 47 (2003), 270–294. [CrossRef] [MathSciNet] [PubMed]

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