Analysis of the Dynamics of a Tumor–Immune System with Chemotherapy and Immunotherapy and Quadratic Optimal Control

作者: Swarnali Sharma , G. P. Samanta

DOI: 10.1007/S12591-015-0250-1

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摘要: In this paper, we consider a tumor growth model with the effect of tumor–immune interactions and chemotherapeutic as well immunotherapeutic drugs. our there are four compartments, namely cells, immune drug concentration concentration. The dynamical behaviour system by analyzing existence stability at various equilibria is discussed elaborately. We set up an optimal control problem relative to so minimize number cells drugs administration. Here use quadratic quantify goal administration chemotherapy controls reduce spread growth. important mathematical findings for also numerically verified using MATLAB. Finally epidemiological implications analytical addressed critically.

参考文章(44)
V KUZNETSOV, I MAKALKIN, M TAYLOR, A PERELSON, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis Bulletin of Mathematical Biology. ,vol. 56, pp. 295- 321 ,(1994) , 10.1016/S0092-8240(05)80260-5
L.G. de Pillis, W. Gu, K.R. Fister, T. Head, K. Maples, A. Murugan, T. Neal, K. Yoshida, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Bellman Prize in Mathematical Biosciences. ,vol. 209, pp. 292- 315 ,(2007) , 10.1016/J.MBS.2006.05.003
L.G De Pillis, A Radunskaya, The dynamics of an optimally controlled tumor model: A case study Mathematical and Computer Modelling. ,vol. 37, pp. 1221- 1244 ,(2003) , 10.1016/S0895-7177(03)00133-X
N. Bellomo, L. Preziosi, Modelling and mathematical problems related to tumor evolution and its interaction with the immune system Mathematical and Computer Modelling. ,vol. 32, pp. 413- 452 ,(2000) , 10.1016/S0895-7177(00)00143-6
John Carl Panetta, K. Renee Fister, Optimal control applied to cell-cycle-specific cancer chemotherapy Siam Journal on Applied Mathematics. ,vol. 60, pp. 1059- 1072 ,(2000) , 10.1137/S0036139998338509
L. G. De Pillis, A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach Journal of Theoretical Medicine. ,vol. 3, pp. 79- 100 ,(2001) , 10.1080/10273660108833067
Alexey S. Matveev, Andrey V. Savkin, Application of optimal control theory to analysis of cancer chemotherapy regimens Systems & Control Letters. ,vol. 46, pp. 311- 321 ,(2002) , 10.1016/S0167-6911(02)00134-2
Gul Zaman, Yong Han Kang, Il Hyo Jung, Stability analysis and optimal vaccination of an SIR epidemic model BioSystems. ,vol. 93, pp. 240- 249 ,(2008) , 10.1016/J.BIOSYSTEMS.2008.05.004
D.E. Kirschner, T.L. Jackson, J.C. Arciero, A mathematical model of tumor-immune evasion and siRNA treatment Discrete and Continuous Dynamical Systems-series B. ,vol. 4, pp. 39- 58 ,(2003) , 10.3934/DCDSB.2004.4.39
Denise Kirschner, John Carl Panetta, Modeling immunotherapy of the tumor-immune interaction. Journal of Mathematical Biology. ,vol. 37, pp. 235- 252 ,(1998) , 10.1007/S002850050127