Geodesic
Delay Dynamics of Cancer and Immune Cell Model
D. Adongo1 ; K.R. Fister1
1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 261-278

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We investigate optimal control of a cancer-immune cell interactive model with delay in the interphase compartment. By applying the optimal control theory, we seek to minimize the cost associated with the chemotherapy drug, minimize the accumulation of cancer cells, and increase the immune cell presence. Optimality conditions and characterization of the control are provided. Numerical analyses are given to enhance the understanding of the difficulties that occur in the control of cancer.
DOI : 10.1051/mmnp/20127112

D. Adongo 1 ; K.R. Fister 1

1 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, USA 
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D. Adongo; K.R. Fister. Delay Dynamics of Cancer and Immune Cell Model. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 261-278. doi: 10.1051/mmnp/20127112

[1] I. Athanassios, D. Barbolosi Compu. Biomedical Res. 2000 211 226

[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 Math. Model. Nat. Phen. 2010 63 71

[5] P. C. Das, R. R. Sharma SIAM J. Control 1971 43 61

[6] L. G. Depillis, A. E. Radunskaya J. Theoretical Medicine 2001 79 100

[7] L. G. Depillis, A. E. Radunskaya Math. Comp. Model. 2003 1221 1244

[8] L. G. Depillis, A. E. Radunskaya, C. L. Wiseman Cancer Research 2005 7950 7958

[9] L. G. Depillis, K. R. Fister, W. Gu, C. Collins, M. Daub, J. Moore, B. Preskill Computational and Math. Methods in Medicine 2009 165 184

[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 Math. Biosci. and Engng. 2007 239 259

[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 Ann. Biomed. Engng 1977 12 33

[15] D. Kirschner, J. C. Panetta J. Math. Bio. 1998 235 252

[16] U. Ledzewicz, T. Brown, H. Schattler Optimization Methods and Software 2004 339 350

[17] U. Ledzewicz, H. Schattler Discrete and Continuous Dynamical Systems - Series B 2006 129 150

[18] D. Mckenzie SIAM News 2004 1 2

[19] J. M. Murray Math. Biosci. 1990 49 67

[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 Bull. of Math. Bio. 1977 317 337

[22] A. Swierniak, U. Ledzewicz, H. Schattler Int. J. Appl. Math. Comput. Sci. 2003 357 368

[23] M. Villasana, A. Radunskaya J. Math. Bio. 2003 270 294

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