Optimal control problems for differential equations applied to tumor growth: state of the art

[1]Alvarez-Arenas, A., Belmonte-Beitia, J. and Calvo, G.F. (2016), Nonlinear waves in a simple model of high-grade glioma, Applied Mathematics and Nonlinear Sciences 1(2), pp. 405-422, doi 10.21042/AMNS.2016.2.00035.Alvarez-ArenasA.Belmonte-BeitiaJ.CalvoG.F.2016Nonlinear waves in a simple model of high-grade gliomaApplied Mathematics and Nonlinear Sciences1240542210.21042/AMNS.2016.2.00035Open DOISearch in Google Scholar

[2]Bellomo, N. and Maini, P. (2007), Challenging mathematical problems in cancer modelling, Mathematical Models and Methods in Applied Sciences 17, pp. 1641-1645, doi 10.1142/S0218202507002418.BellomoN.MainiP.2007Challenging mathematical problems in cancer modellingMathematical Models and Methods in Applied Sciences171641164510.1142/S0218202507002418Open DOISearch in Google Scholar

[3]Belmonte-Beitia, J. (2016), Existence of travelling wave solutions for a Fisher-Kolmogorov system with biomedical applications, Communications in Nonlinear Science and Numerical Simulation 36, pp. 14-20, doi 10.1016/j.cnsns.2015.11.016.Belmonte-BeitiaJ.2016Existence of travelling wave solutions for a Fisher-Kolmogorov system with biomedical applicationsCommunications in Nonlinear Science and Numerical Simulation36142010.1016/j.cnsns.2015.11.016Open DOISearch in Google Scholar

[4]Bergers, G., Hanahan, D. (2008), Modes of resistance to anti-angiogenic therapy, Nature Review of Cancer 8(8), pp. 592-603, doi 10.1038/nrc2442.BergersG.HanahanD.2008Modes of resistance to anti-angiogenic therapyNature Review of Cancer8859260310.1038/nrc2442Open DOISearch in Google Scholar

[5]Betts, J. T. (2010), Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM, Philadelphia doi 10.1137/1.9780898718577.BettsJ. T.2010Practical Methods for Optimal Control and Estimation Using Nonlinear ProgrammingSIAM, Philadelphia10.1137/1.9780898718577Open DOISearch in Google Scholar

[6]Bogdanska, M. U., Bodnar, M., Belmonte-Beitia, J., Murek, M., Schucht, P., Beck, J., Pérez-García, V.M. (2017), A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implications, Mathematical Biosciences 288, pp. 1-13, doi 10.1016/j.mbs.2017.02.003.BogdanskaM. U.BodnarM.Belmonte-BeitiaJ.MurekM.SchuchtP.BeckJ.Pérez-GarcíaV.M.2017A mathematical model of low grade gliomas treated with temozolomide and its therapeutical implicationsMathematical Biosciences28811310.1016/j.mbs.2017.02.003Open DOISearch in Google Scholar

[7]Chisholm, R.H., Lorenzi, T., Lorz, A., Larsen, A.K., de Almeida, L.N., Escargueil, A., Clairambault., J. (2015), Emergence of drug tolerance in cancer cell populations: An evolutionary outcome of selection, nongenetic instability, and stress-induced adaptation, Cancer Research 75, pp. 930-939.ChisholmR.H.LorenziT.LorzA.LarsenA.K.de AlmeidaL.N.EscargueilA.Clairambault. J2015Emergence of drug tolerance in cancer cell populations: An evolutionary outcome of selection, nongenetic instability, and stress-induced adaptationCancer Research7593093910.1158/0008-5472.CAN-14-2103Search in Google Scholar

[8]Coldman A.J. and Goldie. J.H. (1983), A model for the resistance of tumor cells to cancer chemotherapeutic agents, Mathematical Biosciences 65(2), pp. 291-307, doi 10.1016/0025-5564(83)90066-4.ColdmanA.J.GoldieJ.H.1983A model for the resistance of tumor cells to cancer chemotherapeutic agentsMathematical Biosciences65229130710.1016/0025-5564(83)90066-4Open DOISearch in Google Scholar

[9]de Pillis, L.G. and Gu, W. and Fister, K.R. and Head, T. and Maples,K. and Murugan, A. and Neal, T. and Yoshida, K. (2007), Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls, Mathematical Biosciences 209(1), pp. 292-315, doi 10.1016/j.mbs.2006.05.003.de PillisL.G.GuW.FisterK.R.HeadT.MaplesK.MuruganA.NealT.YoshidaK.2007Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controlsMathematical Biosciences209129231510.1016/j.mbs.2006.05.003Open DOISearch in Google Scholar

[10]Dibrov, B.F., Zhabotynsky, A.M., Krinskaya, A.M., Neyfakh, A.V., Yu, A. and Churikova, L.I. (1985), Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic agent administration increasing the selectivity of therapy, Mathematical Biosciences 73, pp. 1-31, doi 10.1016/0025-5564(85)90073-2.DibrovB.F.ZhabotynskyA.M.KrinskayaA.M.NeyfakhA.V.YuA.ChurikovaL.I.1985Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic agent administration increasing the selectivity of therapyMathematical Biosciences7313110.1016/0025-5564(85)90073-2Open DOISearch in Google Scholar

[11]Dołbniak, M. and Świerniak, A. (2013), Comparison of simple models of periodic protocols for combined anticancer therapy, Computational and mathematical methods in medicine 2013, id 567213, pp. 1-11, doi 10.1155/2013/567213.DołbniakM.ŚwierniakA.2013Comparison of simple models of periodic protocols for combined anticancer therapyComputational and mathematical methods in medicine201356721311110.1155/2013/567213Open DOISearch in Google Scholar

[12]d’Onofrio, A., Ledzewicz, U., Maurer, H. and Schättler, H. (2009), On optimal delivery of combination therapy for tumors, Mathematical Biosciences 222(1), pp. 13-26, doi 10.1016/j.mbs.2009.08.004.d’OnofrioA.LedzewiczU.MaurerH.SchättlerH.2009On optimal delivery of combination therapy for tumorsMathematical Biosciences2221132610.1016/j.mbs.2009.08.004Open DOISearch in Google Scholar

[13]Duran, M. R., Podolski-Renic, A., Alvarez-Arenas, A., Dinic, J., Belmonte-Beitia, J., Pesic, M., Perez-Garcia, V. M. (2016), Transfer of drug resistance characteristics between cancer cell subpopulations: A study using simple mathematical models, Bulletin of Mathematical Biology 78(6), pp. 1218-1237, doi 10.1007/s11538-016-0182-0.DuranM. R.Podolski-RenicA.Alvarez-ArenasA.DinicJ.Belmonte-BeitiaJ.PesicM.Perez-GarciaV. M.2016Transfer of drug resistance characteristics between cancer cell subpopulations: A study using simple mathematical modelsBulletin of Mathematical Biology7861218123710.1007/s11538-016-0182-0Open DOISearch in Google Scholar

[14]Eisen, M. (1979), Mathematical Models in Cell Biology and Cancer Chemotherapy, Lectures Notes in Biomathematics, Springer Verlag Berlin, 30.EisenM.1979Mathematical Models in Cell Biology and Cancer ChemotherapyLectures Notes in Biomathematics, Springer VerlagBerlin3010.1007/978-3-642-93126-0Search in Google Scholar

[15]Ergun, A., Camphausen, K.,Wein, L.M. (2003), Optimal scheduling of radiotherapy and angiogenic inhibitors, Bulletin of Mathematical Biology 65, pp. 407-424, doi 10.1016/S0092-8240(03)00006-5.ErgunA.CamphausenK.WeinL.M.2003Optimal scheduling of radiotherapy and angiogenic inhibitorsBulletin of Mathematical Biology6540742410.1016/S0092-8240(03)00006-5Open DOISearch in Google Scholar

[16]Fernández, L.A. and Pola, C. (2014), Catalog of the optimal controls in cancer chemotherapy for the Gompertz model depending on PK/PD and the integral, Discrete Contin. Dyn. Syst. Ser. B 19(6), pp. 1563-1588, doi 10.3934/dcdsb.2014.19.1563.FernándezL.A.PolaC.2014Catalog of the optimal controls in cancer chemotherapy for the Gompertz model depending on PK/PD and the integralDiscrete Contin. Dyn. Syst. Ser. B1961563158810.3934/dcdsb.2014.19.1563Open DOISearch in Google Scholar

[17]Folkman, J. (1971), Tumor angiogenesis: therapeutic implications, New England Journal of Medicine 285(21), pp. 1182-1186, doi 10.1056/NEJM197111182852108.FolkmanJ.1971Tumor angiogenesis: therapeutic implicationsNew England Journal of Medicine285211182118610.1056/NEJM1971111828521084938153Open DOISearch in Google Scholar

[18]Foo, J., Michor, F. (2014), Evolution of acquired resistance to anti-cancer therapy, Journal of Theoretical Biology 355(21), pp. 10-20, doi 10.1016/j.jtbi.2014.02.025.FooJ.MichorF.2014Evolution of acquired resistance to anti-cancer therapyJournal of Theoretical Biology35521102010.1016/j.jtbi.2014.02.025405839724681298Open DOISearch in Google Scholar

[19]Fourer et al. (2003), AMPL: A modeling language for mathematical programming, ThomsonFourer et al2003AMPL: A modeling language for mathematical programming, ThomsonSearch in Google Scholar

[20]Gardner, S.N., Fernandes, M. (2003), New tools for cancer chemotherapy: computational assistance for tailoring treatments, Molecular Cancer Therapeutics 2(10), pp. 1079-84.GardnerS.N.FernandesM.2003New tools for cancer chemotherapy: computational assistance for tailoring treatmentsMolecular Cancer Therapeutics210107984Search in Google Scholar

[21]Hahnfeldt, Philip and Panigrahy, Dipak and Folkman, Judah and Hlatky, Lynn. (1999), Tumor Development under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular Dormancy, Cancer Research 59(19), pp. 4770-4775.HahnfeldtPhilipPanigrahyDipakFolkmanJudahHlatkyLynn.1999Tumor Development under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular DormancyCancer Research591947704775Search in Google Scholar

[22]Ledzewicz, U. and Schättler, H. (2002), Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy, Journal of optimization theory and applications 114(3), pp. 609-637, doi 10.1023/A:1016027113579.LedzewiczU.SchättlerH.2002Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer ChemotherapyJournal of optimization theory and applications114360963710.1023/A:1016027113579Open DOISearch in Google Scholar

[23]Ledzewicz, U. and Schättler, H. (2012), Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments, Journal of Optimization Theory and Applications 153(1), pp. 195–224, doi 10.1007/s10957-011-9954-8.LedzewiczU.SchättlerH.2012Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy TreatmentsJournal of Optimization Theory and Applications153119522410.1007/s10957-011-9954-8Open DOISearch in Google Scholar

[24]Ledzewicz, U. and Schattler, H. and Berman, A. (2009), On the structure of optimal controls for a mathematical model of tumor anti-angiogenic therapy with linear pharmacokinetics, 2009 IEEE Control Applications, (CCA) Intelligent Control, (ISIC) pp. 71-76, doi 10.1109/CCA.2009.5281177.LedzewiczU.SchattlerH.BermanA.2009On the structure of optimal controls for a mathematical model of tumor anti-angiogenic therapy with linear pharmacokinetics2009 IEEE Control Applications, (CCA) Intelligent Control, (ISIC)717610.1109/CCA.2009.5281177Open DOISearch in Google Scholar

[25]Ledzewicz, U., Schättler, H., Gahrooi, M. R. and Dehkordi, S. M. (2013), On the MTD paradigm and optimal control for multi-drug cancer chemotherapy, Mathematical Biosciences and Engineering 10(3), pp. 803-819, doi 10.3934/mbe.2013.10.803.LedzewiczU.SchättlerH.GahrooiM. R.DehkordiS. M.2013On the MTD paradigm and optimal control for multi-drug cancer chemotherapyMathematical Biosciences and Engineering10380381910.3934/mbe.2013.10.803Open DOISearch in Google Scholar

[26]Ledzewicz, U. and Schättler, H. (2006), Drug resistance in cancer chemotherapy as an optimal control problem, Discrete and Continuous Dynamical Systems - Series B 6(1), pp. 129-150, doi 10.3934/dcdsb.2006.6.129.LedzewiczU.SchättlerH.2006Drug resistance in cancer chemotherapy as an optimal control problemDiscrete and Continuous Dynamical Systems - Series B6112915010.3934/dcdsb.2006.6.129Open DOISearch in Google Scholar

[27]Ledzewicz, U., Maurer, H. and Schättler, H. (2011), Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Biosciences and Engineering 8(2), pp. 307-323, doi 10.3934/mbe.2011.8.307.LedzewiczU.MaurerH.SchättlerH.2011Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapyMathematical Biosciences and Engineering8230732310.3934/mbe.2011.8.307Open DOISearch in Google Scholar

[28]Lenhart, S. and Workman, J.T. (2007), Optimal Control Applied to Biological Models, Mathematical and Computational BiologyChapman & Hall/CRCBoca Raton (Fla.)LondonLenhartS.WorkmanJ.T.2007Optimal Control Applied to Biological Models, Mathematical and Computational BiologyChapman & Hall/CRC Boca Raton (Fla.)London10.1201/9781420011418Search in Google Scholar

[29]Louis, David N. and Perry, Arie and Reifenberger, Guido and von Deimling, Andreas and Figarella-Branger, Dominique and Cavenee, Webster K. and Ohgaki, Hiroko and Wiestler, Otmar D. and Kleihues, Paul and Ellison, David W. (2016), The 2016 World Health Organization Classification of Tumors of the Central Nervous System: a summary, Acta Neuropathologica 131(6), pp. 803–820, doi 10.1007/s00401-016-1545-1.LouisDavid N.PerryArieReifenbergerGuidovon DeimlingAndreasFigarella-BrangerDominiqueCaveneeWebster K.OhgakiHirokoWiestlerOtmar D.KleihuesPaulEllisonDavid W.2016The 2016 World Health Organization Classification of Tumors of the Central Nervous System: a summaryActa Neuropathologica131680382010.1007/s00401-016-1545-1Open DOISearch in Google Scholar

[30]Mandonnet E, Delattre JV, Tanguy ML, Swanson KR, Carpentier AF, Duffau H, Cornu P, Van Effenterre R, Alvord EC, and Capelle L. (2003), Continuous growth of mean tumor diameter in a subset of grade ii gliomas, Ann Neurol 53(4), pp. 524–8, doi 10.1002/ana.10528.MandonnetEDelattreJVTanguyMLSwansonKRCarpentierAFDuffauHCornuPVanEffenterre RAlvordECCapelleL.2003Continuous growth of mean tumor diameter in a subset of grade ii gliomasAnn Neurol534524810.1002/ana.10528Open DOISearch in Google Scholar

[31]Martin, R. and Teo, K.L. (1994), Optimal Control of Drug Administration in Cancer ChemotherapyWorld Scientific Press Singapore 1994.MartinR.TeoK.L.1994Optimal Control of Drug Administration in Cancer ChemotherapyWorld Scientific PressSingapore1994Search in Google Scholar

[32]Murray, J. M. (1990), Optimal control for a cancer chemotherapy problem with general growth and loss function, Mathematical Biosciences 98(2), pp. 273-287, doi 10.1016/0025-5564(90)90129-M.MurrayJ. M.1990Optimal control for a cancer chemotherapy problem with general growth and loss functionMathematical Biosciences98227328710.1016/0025-5564(90)90129-MOpen DOISearch in Google Scholar

[33]Panetta, J.C. (1998), A mathematical model of drug resistance: heterogeneous tumors, Mathematical Biosciences 147(1), pp. 41-61, doi 10.1016/S0025-5564(97)00080-1.PanettaJ.C.1998A mathematical model of drug resistance: heterogeneous tumorsMathematical Biosciences1471416110.1016/S0025-5564(97)00080-1Open DOISearch in Google Scholar

[34]Pérez-García, V. M., Calvo, G. F., Belmonte-Beitia, J., Diego, D., Pérez-Romasanta, L. A. (2011), Bright solitary waves in malignant gliomas, Physical Review E . 84, doi 10.1103/PhysRevE.84.021921.Pérez-GarcíaV. M.CalvoG. F.Belmonte-BeitiaJ.DiegoD.Pérez-RomasantaL. A.2011Bright solitary waves in malignant gliomasPhysical Review E8410.1103/PhysRevE.84.02192121929033Open DOISearch in Google Scholar

[35]Pérez-García, V. M., Fitzpatrick, S., Pérez-Romasanta, L. A., Pesic, M., Schucht, P., Arana, E., Sánchez-Gómez, P. (2016), Applied mathematics and nonlinear sciences in the war on cancer, Applied Mathematics and Nonlinear Sciences 1(2), pp. 423-436, doi 10.21042/AMNS.2016.2.00036.Pérez-GarcíaV. M.FitzpatrickS.Pérez-RomasantaL. A.PesicM.SchuchtP.AranaE.Sánchez-GómezP.2016Applied mathematics and nonlinear sciences in the war on cancerApplied Mathematics and Nonlinear Sciences1242343610.21042/AMNS.2016.2.00036Open DOISearch in Google Scholar

[36]Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. and Mishchenko, E. (1962), The Mathematical Theory of Optimal Processes, International Series of Monographs in Pure and Applied MathematicsInterscience PublishersPontryaginL.S.BoltyanskiiV.G.GamkrelidzeR.V.MishchenkoE.1962The Mathematical Theory of Optimal ProcessesInternational Series of Monographs in Pure and Applied Mathematics Interscience Publishers10.1201/9780203749319Search in Google Scholar

[37]Ribba B, Kaloshi G, Peyre M, Ricard D, Calvez V, Tod M, Cajavec-Bernard B, Idbaih A, Psimaras D, Dainese L, Pallud J, Cartalat-Carel S, Delattre J-Y, Honnorat J, Grenier E, and Ducray F. (2012), A Tumor Growth Inhibition Model for Low-Grade Glioma Treated with Chemotherapy or Radiotherapy, Clinical Cancer Research 18(18), pp. 5071–5080, doi 10.1158/1078-0432.CCR-12-0084.RibbaBKaloshiGPeyreMRicardDCalvezVTodMCajavec-BernardBIdbaihAPsimarasDDaineseLPalludJCartalat-CarelSDelattreJ-YHonnoratJGrenierEDucrayF.2012A Tumor Growth Inhibition Model for Low-Grade Glioma Treated with Chemotherapy or RadiotherapyClinical Cancer Research18185071508010.1158/1078-0432.CCR-12-008422761472Open DOISearch in Google Scholar

[38]Rojas, C., Calvo, G. F., Ramis, I., Belmonte-Beitia, J. (2017), Stochastic modelling of slow-progressing tumors: analysis and applications to the cell interplay and control of low grade gliomas, Communications in Nonlinear Science and Numerical Simulation 49, pp. 63-80, doi 10.1016/j.cnsns.2017.02.008.RojasC.CalvoG. F.RamisI.Belmonte-BeitiaJ.2017Stochastic modelling of slow-progressing tumors: analysis and applications to the cell interplay and control of low grade gliomasCommunications in Nonlinear Science and Numerical Simulation49638010.1016/j.cnsns.2017.02.008Open DOISearch in Google Scholar

[39]Rojas, C., and Belmonte-Beitia, J. (2017), Optimizing the delivery of combination therapy for tumors: A mathematical model, International Journal of Biomathematics 10(3), doi 10.1142/S1793524517500395.RojasC.Belmonte-BeitiaJ.2017Optimizing the delivery of combination therapy for tumors: A mathematical modelInternational Journal of Biomathematics10310.1142/S1793524517500395Open DOISearch in Google Scholar

[40]Rojas, C., Belmonte-Beitia, J., Pérez-García, V.M. and Maurer, H. (2016), Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical model, Discrete and Continuous Dynamical Systems - Series B 21(6), pp. 1895-1915, doi 10.3934/dcdsb.2016028.RojasC.Belmonte-BeitiaJ.Pérez-GarcíaV.M.MaurerH.2016Dynamics and optimal control of chemotherapy for low grade gliomas: Insights from a mathematical modelDiscrete and Continuous Dynamical Systems - Series B2161895191510.3934/dcdsb.2016028Open DOISearch in Google Scholar

[41]Schättler, H., and Ledzewicz, U. (2015), Optimal Control for Mathematical Models of Cancer Therapies, Springer New York, 42.SchättlerH.LedzewiczU.2015Optimal Control for Mathematical Models of Cancer Therapies, SpringerNew York4210.1007/978-1-4939-2972-6Search in Google Scholar

[42]Schättler, H. and Ledzewicz, U. (2012), Geometric Optimal Control: Theory, Methods and Examples, Interdisciplinary Applied Mathematics 38, Springer, New York.SchättlerH.LedzewiczU.2012Geometric Optimal Control: Theory, Methods and Examples, Interdisciplinary Applied Mathematics38Springer, New York10.1007/978-1-4614-3834-2Search in Google Scholar

[43]Schättler, H., Ledzewicz, U., Dehkordi, S. M., and Reisi, M. (2012), A geometric analysis of bang-bang extremals in optimal control problems for combination cancer chemotherapy, IEEE Conference on Decision and Control (CDC) pp. 7691-7696, doi 10.1109/CDC.2012.6427077.SchättlerH.LedzewiczU.DehkordiS. M.ReisiM.2012A geometric analysis of bang-bang extremals in optimal control problems for combination cancer chemotherapyIEEE Conference on Decision and Control (CDC)7691769610.1109/CDC.2012.6427077Open DOISearch in Google Scholar

[44]Schimke, R.T. (1984), Gene amplification, drug resistance and cancer, Cancer Research 44, 1735-1742.SchimkeR.T.1984Gene amplification, drug resistance and cancerCancer Research4417351742Search in Google Scholar

[45]Swan, G.W. (1984), Applications of optimal control theory in biomedicine, Monographs and textbooks in pure and applied mathematics M. Dekker.SwanG.W.1984Applications of optimal control theory in biomedicineMonographs and textbooks in pure and applied mathematicsM. DekkerSearch in Google Scholar

[46]Świerniak, A. (1988), Optimal treatment protocols in leukemia-modelling the the proliferation cycle, Proc. of the 12th IMACS World Congress, Paris 4, pp. 170-172.ŚwierniakA.1988Optimal treatment protocols in leukemia-modelling the the proliferation cycleProc. of the 12th IMACS World Congress, Paris4170172Search in Google Scholar

[47]Świerniak, A., Ledzewicz, U. and Schättler, H. (2003), Optimal control for a class of compartmental models in cancer chemotherapy, Int. J. Appl. Math. Comput. Sci 13(3), pp. 257-368.ŚwierniakA.LedzewiczU.SchättlerH.2003Optimal control for a class of compartmental models in cancer chemotherapyInt. J. Appl. Math. Comput. Sci133257368Search in Google Scholar

[48]Świerniak, A. and Polanski, A. and Kimmel, M. (1996), Optimal control problems arising in cell-cycle-specific cancer chemotherapy, Cell Proliferation 29(3), pp. 117–139, doi 10.1046/j.1365-2184.1996.00995.x.ŚwierniakA.PolanskiA.KimmelM.1996Optimal control problems arising in cell-cycle-specific cancer chemotherapyCell Proliferation29311713910.1046/j.1365-2184.1996.00995.xOpen DOISearch in Google Scholar

[49]Świerniak, A. (1995), Cell cycle as an object of control, Journal of Biological Systems 3(1), pp. 41-54, doi 10.1142/S0218339095000058.ŚwierniakA.1995Cell cycle as an object of controlJournal of Biological Systems31415410.1142/S0218339095000058Open DOISearch in Google Scholar

[50]Świerniak, A., Polanski, A. and Kimmel, M. (1996), Optimal control problems arising in cell cycle specific cancer chemotherapy, Cell Proliferation 29(3), pp. 117-139.ŚwierniakA.PolanskiA.KimmelM.1996Optimal control problems arising in cell cycle specific cancer chemotherapyCell Proliferation29311713910.1111/j.1365-2184.1996.tb00100.xSearch in Google Scholar

[51]Świerniak, A., Duda, Z. (1995), Bilinear models of cancer chemoterapy-singularity of optimal solutions, Mathematical population dynamics 2, pp. 347-358.ŚwierniakA.DudaZ.1995Bilinear models of cancer chemoterapy-singularity of optimal solutionsMathematical population dynamics2347358Search in Google Scholar

[52]Vincent, T. L., Brown, J.S. (2007), Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, UKVincentT. L.BrownJ.S.2007Evolutionary Game Theory, Natural Selection, and Darwinian DynamicsCambridge University Press, UKSearch in Google Scholar

[53]Westman, J. J. and Fabijonas, B. R. and Hanson, F. B. (2002), Cancer Treatment Using Multiple Chemotheraputic Agents Subject to Drug Resistance.WestmanJ. J.FabijonasB. R.HansonF. B.2002Cancer Treatment Using Multiple Chemotheraputic Agents Subject to Drug ResistanceSearch in Google Scholar

[54]Wooley, T. E., Belmonte-Beitia, J., Calvo, G. F., Hopewell, J. W., Gaffney, E. A. and Jones, B. (2018), Changes in the retreatment radiation tolerance of the spinal cord with time after the initial treatment, International Journal of Radiation Biology 94(6), pp. 515-531, doi 10.1080/09553002.2018.1430911.WooleyT. E.Belmonte-BeitiaJ.CalvoG. F.HopewellJ. W.GaffneyE. A.JonesB.2018Changes in the retreatment radiation tolerance of the spinal cord with time after the initial treatmentInternational Journal of Radiation Biology94651553110.1080/09553002.2018.143091129620431Open DOISearch in Google Scholar