Open Access
| Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Cancer modelling
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 13 | |
| DOI | https://doi.org/10.1051/mmnp/2020057 | |
| Published online | 08 February 2021 | |
- A. Chorobura and H. Zidani, Bi-objective finite horizon optimal control problems with Bolza and maximum running cost. Available at: Hal 01929094 (2018). [Google Scholar]
- L.G. de Pillis, K.R. Fister, W. Gu, T. Head, K. Maples, T. Neal and K. Kozai, Optimal control of mixed immunotherapy and chemotherapy of tumors. J. Biol. Syst. 16 (2008) 51–80. [Google Scholar]
- L.G. de Pillis, W. Gu and A.E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 238 (2006) 841–862. [CrossRef] [Google Scholar]
- L.G. de Pillis, A.E. Radunskaya and C.L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res. 65 (2005) 7950–7958. [Google Scholar]
- L.G. de Pillis, W. Gu, K.R. Fister, T. Head, K. Maples, A. Murugan and K. Yoshida, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209 (2007) 292–315. [Google Scholar]
- J.A. Désidéri and R. Duvigneau, Optimisation Avancée Support de cours de la partie Optimisation Fonctionnelle, Polytech’Nice (2016). [Google Scholar]
- D.S. Dixit, D. Kumar, S. Kumar and R. Johri, A mathematical model of chemotherapy for tumor treatment. Adv. Appl. Math. Biosci. 3 (2012) 1–10. [Google Scholar]
- M. Ehrgott, Multicriteria Optimization, 2nd ed. Springer, New York, USA (2005). [Google Scholar]
- W. Fleming and R. Rishel, Deterministic and Stochastic Optimal Control. Springer New York (1975). [Google Scholar]
- A. Hanoteau, C. Henin and M. Moser, L’immunothérapie au service de la chimiothérapie, de nouvelles avancées. Médecine/Sciences 32 (2016) 353–361. [EDP Sciences] [Google Scholar]
- A. Kumar and A. Vladimirsky, An efficient method for multiobjective optimal control and optimal control subject to integral constraints. J. Comput. Math. 28 (2010) 517–551. [Google Scholar]
- V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor and A.S. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56 (1994) 295–321. [Google Scholar]
- H. Kwakernaak, R. Sivan and B.N.D. Tyreus, Linear optimal control systems. J. Dyn. Syst. Measur. Control 96 (1974) 373–374. [Google Scholar]
- U. Ledzewicz and H. Schättler, Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Control Optim. 46 (2017) 1052–79. [Google Scholar]
- R.B. Martin, M.E. Fisher, R.F. Minchin and K.L. Teo, A mathematical model of cancer chemotherapy with an optimal selection of parameters. Math. Biosci. 99 (1990) 205–230. [Google Scholar]
- K. Miettinen, Nonlinear Multiobjective Optimization. Springer, Berlin, Germany (2012). [Google Scholar]
- S. Sabir and N. Raissi, Analysis of tumor/effector cell dynamics and decision support in therapy. In Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics (2019) 153–164. [Google Scholar]
- S. Sabir, N. Raissi and M. Serhani, Chemotherapy and immunotherapy for tumors: a study of quadratic optimal control. Int. J. Appl. Comput. Math. 6 (2020) 81. [Google Scholar]
- H.M. Schattler and U. Ledzewicz, Optimal control for mathematical models of cancer therapies. Vol. 42 of Interdisciplinary Applied Mathematics. Springer, New York (2015). [Google Scholar]
- M. Serhani, H. Essaadi, K. Kassara and A. Boutoulout, Control by viability in a chemotherapy cancer model. Acta Biotheor. 67 (2019) 177–200. [PubMed] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.