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] [Google Scholar]
  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. [Google Scholar]
  3. W. Cheney, D. Kincaid. Numerical mathematics and computing. Thomson Brooks/Cole, Belmont, 2008. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  10. R. D. Driver. Ordinary and delay differential equations. Springer-Verlag, New York, 1977. [Google Scholar]
  11. R. Fletcher. Practical methods of optimization. Wiley and Sons, New York, 1987. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  15. D. Kirschner, J. C. Panetta. Modeling immunotherapy of the tumor-immune interaction. J. Math. Bio., 35 (1998), 235–252. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  18. D. McKenzie. Mathematical modeling and cancer. SIAM News, 31 (2004), 1–2. [Google Scholar]
  19. J. M. Murray. Some optimality control problems in cancer chemotherapy with a toxicity limit. Math. Biosci., 100 (1990), 49–67. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  20. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko. The mathematical theory of optimal processes. Gordon and Breach, 1962. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  23. M. Villasana A. Radunskaya. A delay differential equation model for tumor growth. J. Math. Bio., 47 (2003), 270–294. [Google Scholar]

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