The influence of fixed and free final time of treatment on optimal chemotherapeutic protocols

Mathematical and Computer Modelling

Volumn 27, Issue 6, 1998, Pages 59-72

  Boldrini, J L ^a   Costa, M I S ^b  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Chemotherapeutic treatments; Fixed and free final time; Optimal control

Indexed keywords

EID: 0032031153     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(98)00029-6     Document Type: Article

References (13)

1. gG multiple myeloma, Bull. Math. Biol. 39, 317-337, (1977).
2. 2. G.W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosc. 101, 237-284, (1990).
3. 3. A. Świerniak, Some control problems for simplest differential models of proliferation cycle, Appl. Math. Comp. Sci. 4, 223-232, (1994).
4. 4. A. Świerniak and Z. Duda, Singularity of optimal control in some problems related to optimal chemotherapy, Mathl. Comput. Modelling 19 (6-8), 255-262, (1994).
5. 5. D. Kirk, Optimal Control Theory, Prentice Hall, (1970).
6. 6. M.I.S. Costa, J.L. Boldrini and R.C. Bassanezi, Optimal chemical control of populations developing drug resistance, IMA J. Math. Appl. Med. Biol. 9, 215-226, (1992).
7. 7. M.I.S. Costa, J.L. Boldrini and R.C. Bassanezi, Optimal chemotherapy: A case study with drug resistance, saturation effect and toxicity, IMA J. Math. Appl. Med. Biol. 11, 45-59, (1994).
8. 8. M.I.S. Costa, J.L. Boldrini and R.C. Bassanezi, Drug kinetics and drug resistance in optimal chemotherapy, Math. Biosc. 125, 191-209, (1995).
9. 9. M.I.S. Costa, J.L. Boldrini and R.C. Bassanezi, Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity, Math. Biosci. 125, 211-228, (1995).
10. 10. R.P. Hämäläinen, J. Hämäläinen and U. Miekkal, Optimal control modelling of ventricular ejection - Do the endpoint conditions dominate the perfomance criteria?, In Modelling and Data Analysis in Biotechnology and Medical Engineering, (Edited by G.G. Vansteenkiste and P.C. Young), North-Holland, (1983).
11. nd edition, Krieger, Huntington, NY, (1980).
12. 12. E.B. Lee and L. Markus, Foundations of Optimal Control Theory, Wiley, New York, (1967).
13. 13. A.P. Sage, Optimum System Control, Prentice Hall, Englewood Cliffs, NJ, (1968).