Controllability of a model of combined anticancer therapy

Control and Cybernetics

Volumn 42, Issue 1, 2013, Pages 123-138

  Klamka, Jerzy ^a   Swierniak, Andrzej ^a  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Biomathematical modelling; Cancer therapy; Controllability; Semilinear systems

Indexed keywords

EID: 85018222592     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Bartha K. and H. Rieger (2006) Vascular network remodeling via vessel cooption, regression and growth in tumors. J. Theor. Biol. 241, 903-918.
2. Camidge D.R. and D.I. Jordell (2005) Introduction to the cellular and molecular biology of cancer, chapter 24: Chemotherapy, Oxford University Press.
3. d'Onofrio A. and A. Gandolfi (2004) Tumour eradication by antiangiogenic therapy analysis and extensions of the model by Hahnfeldt et al. (1999) Math. Biosci 191, 159-184.
4. d'Onofrio A. and A. Gandolfi (2009) A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy. Math. Med. Biol. 26 (1), 63-95.
5. Ergun A., K. Camphausen, and L.M. Wein (2003) Optimal scheduling of radiotherapy and angio-genic inhibitors. Bull. Math. Biol. 65, 407-424.
6. Folkman J. (1971) Tumor angiogenesis: therapeutic implications. N. Engl. J. Med. 295, 1182-1186.
7. Forys U. and J. Poleszczuk (2011) A delay-differential equation model of HIV related cancer-immune system dynamics. Math. Biosci. Engineering, 8 (2), 627-641
8. Hahnfeldt P., D. Panigraphy, J. Folkman and L. Hlatky (1999) Tumor development under angiogenic signaling: A dynamic theory of tumor growth, treatment response and postvascular dormacy. Cancer Res. 59, 4770-4778.
9. Kaczorek T. (1993) Linear Control Systems, vol. I and vol. II. Research Studies Press and John Wiley, New York.
10. Kaczorek T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London.
11. Kaczorek T. (2007) Polynomial and Rational Matrices. Applications in Dy- namical Systems Theory. Springer-Verlag, London.
12. Kerbel R.S. (1997) A cancer therapy resistant to resistance. Nature, 390, 335-340.
13. Klamka J. (1991) Controllability of Dynamical Systems. Kluwer Academic Publishers, Dordrecht, The Netherlands.
14. Klamka J. (1993) Controllability of dynamical systems-a survey. Archives of Control Sciences, 2(3/4), 281-307.
15. Klamka J. (1996) Constrained controllability of nonlinear systems. Journal of Mathematical Analysis and Applications 201(2), 365-374.
16. Klamka J. (2004) Constrained controllability of semilinear systems with multiple delays in control. Bulletin of the Polish Academy of Sciences. Technical Sciences. 52 (1), 25-30.
17. Ledzewicz U. and H. Schättler (2007) Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Contr. Optim, 46, 1052-1079.
18. Ledzewicz U. and H. Schättler (2008) Analysis of mathematical model for tumor anti-angiogenesis. Optim. Contr. Appl. Meth., 29, 41-57.
19. Świerniak A. (2008) Direct and indirect control of cancer populations. Bulletin of the Polish Academy of Sciences Technical Sciences 56, 367-368.
20. Swierniak A. (2009) Comparison of six models of antiangiogenic therapy. Applicationes Mathematicae, 36, 333-348.
21. Swierniak A (2012) Combined anticancer therapy as a control problem. In: M. Bus lowicz and K. Malinowski, eds., Advances in Control Theory and Automation. Monograph of Committee of Automatics and Robotics PAS, Bia lystok, 251-263.
22. Swierniak A. (2012a) Control problems related to three compartmental model of combined anticancer therapy. Proceedings. 20 IEEE Mediterrenean Conference on Automation and Control MED 12, Barcelona. IEEE Press, 1428-1433.
23. Swierniak A. and K. Ploskonski (2010) Periodic control of antiangiogenic and combined anticancer therapies. IFAC Workshop of Periodic Control Systems PSYCO 2010, Antalya, CD ROM edition.
24. Swierniak A. and J. Klamka (2011) Control properties of models of antiangiogenic therapy. In: K. Malinowski and R. Dindorf, eds., Advances in Automatics and Robotics (Posţepy Automatyki i Robotyki). Monograph of Committee of Automatics and Robotics PAS, 16, Kielce, part 2, 300-312.