Article
Optimal control problems for differential equations applied to tumor growth: state of the art
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Abstract
In this manuscript, we shall apply the tools and methods from optimal control to analyze various minimally parameterized models that describe the dynamics of populations of cancer cells and elements of the tumor microenvironment under different anticancer therapies. In spite of their simplicity, the analysis of these models that capture the essence of the underlying biology sheds light on more general scenarios and, in many cases, leads to conclusions that confirm experimental studies and clinical data. We focus on four applications: optimal control applied to compartmental models, brain tumors, drug resistance and antiangiogenic treatment.
Keywords
Optimal control, chemotherapy, bang-bang and singular controls, Pontryagin maximum principle, 92-02, 49J15, 49J30, 92B99, 93B27, 93C15
Citation
Rojas, C. & Belmonte-Beitia, J. (2018). Optimal control problems for differential equations applied to tumor growth: State of the art. Applied Mathematics and Nonlinear Sciences, 3(2), 375–402. https://doi.org/10.21042/AMNS.2018.2.00029
C. Rojas and J. Belmonte-Beitia, “Optimal control problems for differential equations applied to tumor growth: State of the art,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, pp. 375–402, 2018, doi: 10.21042/AMNS.2018.2.00029.
Rojas C, Belmonte-Beitia J. Optimal control problems for differential equations applied to tumor growth: State of the art. Applied Mathematics and Nonlinear Sciences. 2018;3(2):375–402. doi:10.21042/AMNS.2018.2.00029.
Rojas, C. and Belmonte-Beitia, J. (2018), ‘Optimal control problems for differential equations applied to tumor growth: State of the art’, Applied Mathematics and Nonlinear Sciences, 3(2), pp. 375–402. Available at: https://doi.org/10.21042/AMNS.2018.2.00029.
Rojas, Clara, and Juan Belmonte-Beitia. “Optimal Control Problems for Differential Equations Applied to Tumor Growth: State of the Art.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, 2018, pp. 375–402. https://doi.org/10.21042/AMNS.2018.2.00029.
Rojas, Clara, and Juan Belmonte-Beitia. “Optimal Control Problems for Differential Equations Applied to Tumor Growth: State of the Art.” Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 375–402. https://doi.org/10.21042/AMNS.2018.2.00029.
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