Optimal control in a mathematical model for leukemia therapy with phase constraints

Moscow University Computational Mathematics and Cybernetics - Tập 36 Số 4 - Trang 178-182 - 2012
Alexander S. Bratus1, A. S. Goncharov1, I. T. Todorov2
1Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
2Mannheim University of Applied Sciences, Mannheim, Germany

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Tài liệu tham khảo

E. K. Afenya and C. P. Calderon, “A Brief Look at Normal Cells Decline and Inhibition in Acute Leukemia,” J. Can. Det. Prev. 20(3), 171–191 (1996).

C. L. Frenzen and J. D. Murray, “A Cell Kinetics Justification for Gompertz Equation,” SIAM J. Appl. Math. 46, 614–624 (1986).

M. Gyllenberg and G. F. Webb, “Quiescence As An Explanation of Gompertzian Tumor Growth,” Growth Dev. Aging 53(1), 25–33 (1989).

W. S. Kendal, “Gompertzian Growth As a Consequence of Tumor Heterogeneity,” Math. Biosci. 73, 103–107 (1985).

A. K. Laird, “Dynamics of Tumor Growth: Comparison of Growth and Cell Population Dynamics,” Math. Biosci. 185, 153–167 (2003).

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986).

F. P. Vasil’ev, Optimization Methods (MTsNMO, Moscow, 2011) [in Russian].

N. N. Moiseev, Elements of the Theory of Optimal Systems (Nauka, Moscow, 1975) [in Russian].

A. S. Bratus, E. Fimmel, F. Nurnberg, and Y. Todorov, “On Strategies on a Mathematical Model for Leukemia Therapy,” Nonlinear Analysis: Real World Applications 13, 1044–1059 (2011).