-
1
-
-
1042279443
-
Hopf point analysis for angiogenesis models
-
Z. Agur, L. Arakelyan, P. Daugulis and Y. Ginosar, Hopf point analysis for angiogenesis models, Discrete and Continuous Dynamical Systems, Series B, 4 (2004), 29-38.
-
(2004)
Discrete and Continuous Dynamical Systems, Series B
, vol.4
, pp. 29-38
-
-
Agur, Z.1
Arakelyan, L.2
Daugulis, P.3
Ginosar, Y.4
-
2
-
-
0032170064
-
Continuous and discrete mathematical models of tumorinduced angiogenesis
-
A. Anderson and M. Chaplain, Continuous and discrete mathematical models of tumorinduced angiogenesis, Bull. Math. Biol., 60 (1998), 857ff.
-
(1998)
Bull. Math. Biol.
, vol.60
, pp. 857
-
-
Anderson, A.1
Chaplain, M.2
-
3
-
-
11844254028
-
Singular trajectories and their role in control theory
-
Springer Verlag
-
B. Bonnard and M. Chyba, "Singular Trajectories and their Role in Control Theory," Springer Verlag, Series: Mathematics and Applications, Vol.40, 2003.
-
(2003)
Series: Mathematics and Applications
, vol.40
-
-
Bonnard, B.1
Chyba, M.2
-
6
-
-
33746656314
-
Optimal control in a model of dendritic cell transfection cancer immunotherapy
-
F. Castiglione and B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bulletin of Mathematical Biology, 68 (2006), 255-274.
-
(2006)
Bulletin of Mathematical Biology
, vol.68
, pp. 255-274
-
-
Castiglione, F.1
Piccoli, B.2
-
7
-
-
0035738977
-
A mathematical tumor model with immune resistance and drug therapy: An optimal control approach
-
L. G. de Pillis and A. Radunskaya, .A mathematical tumor model with immune resistance and drug therapy: An optimal control approach, J. of Theoretical Medicine, 3 (2001), 79-100
-
(2001)
J. of Theoretical Medicine
, vol.3
, pp. 79-100
-
-
De Pillis, L.G.1
Radunskaya, A.2
-
8
-
-
23144445934
-
A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences
-
A. d'Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D, 208 (2005), 220-235.
-
(2005)
Physica D
, vol.208
, pp. 220-235
-
-
D'Onofrio, A.1
-
9
-
-
4444221249
-
Tumour eradication by antiangiogenic therapy: Analysis and extensions of the model by Hahnfeldt et al. (1999)
-
A. d'Onofrio and A. Gandolfi, Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999), Math. Biosci., 191 (2004), 159-184
-
Math. Biosci.
, vol.191
, Issue.2004
, pp. 159-184
-
-
D'Onofrio, A.1
Gandolfi, A.2
-
10
-
-
0003297714
-
Mathematical models in cell biology and cancer chemotherapy
-
Springer Verlag
-
M. Eisen, "Mathematical Models in Cell Biology and Cancer Chemotherapy," Lecture Notes in Biomathematics, Vol.30, Springer Verlag, 1979.
-
(1979)
Lecture Notes in Biomathematics
, vol.30
-
-
Eisen, M.1
-
11
-
-
0037406640
-
Optimal scheduling of radiotherapy and angiogenic inhibitors
-
A. Ergun, K. Camphausen and L. M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. of Math. Biology, 65 (2003), 407-424
-
(2003)
Bull. of Math. Biology
, vol.65
, pp. 407-424
-
-
Ergun, A.1
Camphausen, K.2
Wein, L.M.3
-
12
-
-
0033687699
-
Optimal control applied to cell-cycle-specific cancer chemotherapy
-
K. R. Fister and J. C. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy, SIAM J. Appl. Math., 60 (2000), 1059-1072.
-
(2000)
SIAM J. Appl. Math.
, vol.60
, pp. 1059-1072
-
-
Fister, K.R.1
Panetta, J.C.2
-
13
-
-
34247401423
-
Critical-point analysis for three-variable cancer angiogenesis models
-
U. Forys, Y. Keifetz and Y. Kogan, Critical-point analysis for three-variable cancer angiogenesis models, Mathematical Biosciences and Engineering, 2 (2005), 511-525.
-
(2005)
Mathematical Biosciences and Engineering
, vol.2
, pp. 511-525
-
-
Forys, U.1
Keifetz, Y.2
Kogan, Y.3
-
14
-
-
35148853137
-
Sufficient conditions for a strong minimum in singular control problems
-
H. Gardner-Moyer, Sufficient conditions for a strong minimum in singular control problems, SIAM J. Control, 11 (1973), 620-636.
-
(1973)
SIAM J. Control
, vol.11
, pp. 620-636
-
-
Gardner-Moyer, H.1
-
15
-
-
0033213978
-
Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy
-
P. Hahnfeldt, D. Panigrahy, J. Folkman and L. Hlatky, Tumor development under angiogenic signaling: A dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Research, 59 (1999), 4770-4775.
-
(1999)
Cancer Research
, vol.59
, pp. 4770-4775
-
-
Hahnfeldt, P.1
Panigrahy, D.2
Folkman, J.3
Hlatky, L.4
-
16
-
-
0031443206
-
A cancer therapy resistant to resistance
-
R. S. Kerbel, A cancer therapy resistant to resistance, Nature, 390 (1997), 335-336.
-
(1997)
Nature
, vol.390
, pp. 335-336
-
-
Kerbel, R.S.1
-
17
-
-
0000916037
-
The high-order maximal principle and its application to singular controls
-
A. Krener, The high-order maximal principle and its application to singular controls, SIAM J. Control and Optimization, 15 (1977), 256-293.
-
(1977)
SIAM J. Control and Optimization
, vol.15
, pp. 256-293
-
-
Krener, A.1
-
19
-
-
33847219672
-
A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors
-
Sevilla, Spain, December
-
U. Ledzewicz and H. Schättler, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, Proceedings of the 44th IEEE Conference on Decision and Control (CDC) and European Control Conference ECC'05, Sevilla, Spain, December 2005, 934-939
-
(2005)
Proceedings of the 44th IEEE Conference on Decision and Control (CDC) and European Control Conference ECC'05
, pp. 934-939
-
-
Ledzewicz, U.1
Schättler, H.2
-
20
-
-
33947585997
-
Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy
-
U. Ledzewicz and H. Schättler, Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy, Mathematical Biosciences, 206 (2007), 320-342.
-
(2007)
Mathematical Biosciences
, vol.206
, pp. 320-342
-
-
Ledzewicz, U.1
Schättler, H.2
-
21
-
-
34247372535
-
On a class of systems describing tumor anti-angiogenesis under Gompertzian growth
-
U. Ledzewicz and H. Schättler, On a class of systems describing tumor anti-angiogenesis under Gompertzian growth, WSEAS Transactions on Systems, 4 (2007), 758-766
-
(2007)
WSEAS Transactions on Systems
, vol.4
, pp. 758-766
-
-
Ledzewicz, U.1
Schättler, H.2
-
22
-
-
42749090784
-
Anti-angiogenic therapy in cancer treatment as an optimal control problem
-
U. Ledzewicz and H. Schättler, Anti-angiogenic therapy in cancer treatment as an optimal control problem, SIAM J. on Control and Optimization, 46 (2007), 1052-1079.
-
(2007)
SIAM J. on Control and Optimization
, vol.46
, pp. 1052-1079
-
-
Ledzewicz, U.1
Schättler, H.2
-
23
-
-
40449120191
-
Analysis of a mathematical model for tumor anti-angiogenesis
-
U. Ledzewicz and H. Schattier, Analysis of a mathematical model for tumor anti-angiogenesis, Optimal Control Appl. and Methods, 29 (2008), 41-57.
-
(2008)
Optimal Control Appl. and Methods
, vol.29
, pp. 41-57
-
-
Ledzewicz, U.1
Schattier, H.2
-
24
-
-
42749096482
-
Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis
-
U. Ledzewicz and H. Schättler, Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis, J. of Theoretical Biology, 252 (2008), 295-312.
-
(2008)
J. of Theoretical Biology
, vol.252
, pp. 295-312
-
-
Ledzewicz, U.1
Schättler, H.2
-
25
-
-
67650907335
-
Minimization of the tumor volume and endothelial support for a system describing tumor anti-angiogenesis
-
U. Ledzewicz and H. Schättler, Minimization of the tumor volume and endothelial support for a system describing tumor anti-angiogenesis, WSEAS Transactions on Biology and Biomedicine, 5 (2008), 23-33
-
(2008)
WSEAS Transactions on Biology and Biomedicine
, vol.5
, pp. 23-33
-
-
Ledzewicz, U.1
Schättler, H.2
-
26
-
-
21244449627
-
Optimization techniques for the verification of second-order sufficient conditions for bang-bang controls
-
H. Maurer, G. Büskens, J.-H. Kim and Y. Kaja, Optimization techniques for the verification of second-order sufficient conditions for bang-bang controls, Optimal Control, Applications and Methods, 26 (2005), 129-156.
-
(2005)
Optimal Control, Applications and Methods
, vol.26
, pp. 129-156
-
-
Maurer, H.1
Büskens, G.2
Kim, J.-H.3
Kaja, Y.4
-
27
-
-
0003716451
-
-
MacMillan, New York
-
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes," MacMillan, New York, 1964.
-
(1964)
The Mathematical Theory of Optimal Processes
-
-
Pontryagin, L.S.1
Boltyanskii, V.G.2
Gamkrelidze, R.V.3
Mishchenko, E.F.4
-
28
-
-
0035953488
-
Simple ODE models of tumor growth and antiangiogenic or radiation treatment
-
R. K. Sachs, L. R. Hlatky and P. Hahnfeldt, Simple ODE models of tumor growth and antiangiogenic or radiation treatment, Math. Comput. Mod., 33 (2001), 1297-1305.
-
(2001)
Math. Comput. Mod.
, vol.33
, pp. 1297-1305
-
-
Sachs, R.K.1
Hlatky, L.R.2
Hahnfeldt, P.3
-
29
-
-
1542318597
-
On sufficient optimality conditions for singular extremals
-
Maui, Hi, USA, December
-
G. Stefani, On sufficient optimality conditions for singular extremals, Proceedings of the 42nd IEEE Conference on Decision and Control (CDC), Maui, Hi, USA, December 2003, 2746-2749.
-
(2003)
Proceedings of the 42nd IEEE Conference on Decision and Control (CDC)
, pp. 2746-2749
-
-
Stefani, G.1
-
30
-
-
0025049681
-
Role of optimal control in cancer chemotherapy
-
G. W. Swan, Role of optimal control in cancer chemotherapy, Math. Biosci., 101 (1990), 237-284.
-
(1990)
Math. Biosci.
, vol.101
, pp. 237-284
-
-
Swan, G.W.1
-
31
-
-
67650875107
-
Optimal treatment protocols in leukemia - Modelling the proliferation cycle
-
Paris
-
A. Swierniak, Optimal treatment protocols in leukemia - modelling the proliferation cycle, Proceedings of the 12th IMACS World Congress, Paris, 4 (1988), 170-172.
-
(1988)
Proceedings of the 12th IMACS World Congress
, vol.4
, pp. 170-172
-
-
Swierniak, A.1
-
32
-
-
0002747592
-
Cell cycle as an object of control
-
A. Swierniak, Cell cycle as an object of control, J. of Biological Systems, 3 (1995), 41-54.
-
(1995)
J. of Biological Systems
, vol.3
, pp. 41-54
-
-
Swierniak, A.1
-
33
-
-
33644539123
-
Optimal control for a class of compartmental models in cancer chemotherapy
-
A. Swierniak, U. Ledzewicz and H. Schattier, Optimal control for a class of compartmental models in cancer chemotherapy, Int. J. Applied Mathematics and Computer Science, 13 (2003), 357-368.
-
(2003)
Int. J. Applied Mathematics and Computer Science
, vol.13
, pp. 357-368
-
-
Swierniak, A.1
Ledzewicz, U.2
Schattier, H.3
-
34
-
-
0029938149
-
Optimal control problems arising in cell-cycle-specific cancer chemotherapy
-
A. Swierniak, A. Polanski and M. Kimmel, Optimal control problems arising in cell-cycle-specific cancer chemotherapy, Cell prolif., 29 (1996), 117-139.
-
(1996)
Cell Prolif.
, vol.29
, pp. 117-139
-
-
Swierniak, A.1
Polanski, A.2
Kimmel, M.3
-
35
-
-
38349139013
-
Optimization of angiogenic therapy as optimal control problem
-
Acta Press, Ed. M. Doblare
-
A. Swierniak, G. Gala, A. Gandolfi and A. d'Onofrio, Optimization of angiogenic therapy as optimal control problem, Proceedings of the 4th IASTED Conference on Biomechanics, Acta Press, (Ed. M. Doblare), (2006), 56-60.
-
(2006)
Proceedings of the 4th IASTED Conference on Biomechanics
, pp. 56-60
-
-
Swierniak, A.1
Gala, G.2
Gandolfi, A.3
D'Onofrio, A.4
-
36
-
-
57749120581
-
Direct and indirect control of cancer populations
-
A. Swierniak, Direct and indirect control of cancer populations, Bulletin of the Polish Academy of Sciences, Technical Sciences, 56, (2008), 367-378.
-
(2008)
Bulletin of the Polish Academy of Sciences, Technical Sciences
, vol.56
, pp. 367-378
-
-
Swierniak, A.1
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