[1] R. B. Martin, M. E. Fisher, R. F. Minchin, K. L. Teo, Low-intensity combination chemotherapy maximizes host survival time for tumors containing drug-resistant cells, Math. Biosc., 110 (1992), 221–252. doi: 10.1016/0025-5564(92)90039-Y
[2] S. T. R. Pinho, D. S. Rodrigues, P. F. de A. Mancera, A mathematical model of chemotherapy response to tumor growth, Can. Appl. Math. Q., 4 (2011), 369–384.
[3] S. T. R. Pinho, F. S. Bacelar, R. F. S. Andrade, H. I. Freedman, A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy, Nonlin. Anal.: Real World Appl., 14 (2013), 815–828. doi: 10.1016/j.nonrwa.2012.07.034
[4] D. S. Rodrigues, S. T. R. Pinho, P. F. de A. Mancera, Um modelo matemático em quimioterapia, TEMA Tend. Mat. Appl. Comput., 13 (2012), 1–12. doi: 10.5540/tema.2012.013.01.0001
[5] J. C. Panetta, K. R. Fister, Optimal control applied to competing chemotherapeutic cell-kill strategies, SIAM J. Appl. Math., 63 (2003), 1954–1971. doi: 10.1137/S0036139902413489
[6] L. G. de Pillis, A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: An optimal control approach, J. Theor. Med., 3 (2001), 79–100. doi: 10.1080/10273660108833067
[7] L. G. de Pillis, W. Gu, K. R. Fister, T. Head, K. Maples, A. Murugan, et al., Chemotherapy for tumors: An analysis of the dynamics and a study of quadratic and linear optimal controls, Math. Biosc., 209 (2007), 292–315. doi: 10.1016/j.mbs.2006.05.003
[8] A. D’Onofrio, U. Ledzewicz, H. Maurer, H. Schättler, On optimal delivery of combination therapy for tumors, Math. Biosc., 222 (2009), 13–26. doi: 10.1016/j.mbs.2009.08.004
[9] G. S. Stamatakos, E. A. Kolokotroni, D. D. Dionysiou, E. C. Georgiadi, C. Desmedt, An advanced discrete state-discrete event multiscale simulation model of the response of a solid tumor to chemotherapy: Mimicking a clinical study, J. Theor. Biol., 266 (2010), 124–139. doi: 10.1016/j.jtbi.2010.05.019
[10] L. G. Marcu, E. Bezak, Neoadjuvant cisplatin for head and neck cancer: Simulation of a novel schedule for improved therapeutic ratio, J. Theor. Biol., 297 (2012), 41–47. doi: 10.1016/j.jtbi.2011.12.001
[11] S. T. R. Pinho, H. I. Freedman, F. Nani, A chemotherapy model for the treatment of cancer with metastasis, Math. Comp. Model., 36 (2002), 773–803. doi: 10.1016/S0895-7177(02)00227-3
[12] D. S. Rodrigues, P. F. de A. Mancera, Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response, Math. Biosci. Eng., 10 (2013), 221–234. doi: 10.3934/mbe.2013.10.221
[13] M. Mamat, K. A. Subiyanto, A. Kartono, Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy, Appl. Math. Sci., 7 (2013), 247–261. doi: 10.12785/amis/070131
[14] J. Malinzi, Mathematical analysis of a mathematical model of chemovirotherapy: Effect of drug infusion method, Comput. Math. Methods Med., 2019 (2019), 7576591.
[15] P. Unni, P. Seshaiyer, Mathematical modeling, analysis, and simulation of tumor dynamics with drug interventions, Comput. Math. Methods Med., 2019 (2019), 4079298.
[16] W. L. Duan, The stability analysis of tumor-immune responses to chemotherapy system driven by Gaussian colored noises, Chaos Solitons Fractals, 141 (2020), 110303. doi: 10.1016/j.chaos.2020.110303
[17] W. L. Duan, H. Fang, The unified colored noise approximation of multidimensional stochastic dynamic system, Phys. A, 555 (2020), 124624. doi: 10.1016/j.physa.2020.124624
[18] W. L. Duan, H. Fang, C. Zeng, The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises, Chaos Solitons Fractals, 127 (2019), 96–102. doi: 10.1016/j.chaos.2019.06.030
[19] P. M. Altrock, L. L. Liu, F. Michor, The mathematics of cancer: integrating quantitative models, Nat. Rev. Cancer, 15 (2015), 730–745. doi: 10.1038/nrc4029
[20] A. Fasano, A. Bertuzzi, A. Gandolfi, Mathematical modelling of tumour growth and treatment, Complex Syst. Biomed., 2006.
[21] A. Yin, D. J. A. R. Moes, J. G. C. van Hasselt, J. J. Swen, H. J. Guchelaar, A Review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors, CPT Pharmacometrics Syst. Pharmacol., 8 (2019), 720–737. doi: 10.1002/psp4.12450
[22] L. Parajdi, Modeling the treatment of tumor cells in a solid tumor, J. Nonlinear Sci. Appl., 7 (2014), 188–195. doi: 10.22436/jnsa.007.03.05
[23] A. Cucuianu, R. Precup, A hypothetical-mathematical model of acute myeloid leukaemia pathogenesis, Comput. Math. Methods Med., 11 (2010), 49–65. doi: 10.1080/17486700902973751
[24] D. Dingli, F. Michor, Successful therapy must eradicate cancer stem cells, Stem. Cells, 24 (2006), 2603–2610. doi: 10.1634/stemcells.2006-0136
[25] L. G. Parajdi, R. Precup, E. A. Bonci, C. Tomuleasa, A mathematical model of the transition from normal hematopoiesis to the chronic and accelerated-acute stages in myeloid leukemia, Mathematics, 8 (2020), 376. doi: 10.3390/math8030376
[26] F. J. Richards, A flexible growth function for empirical use, J. Exp. Bo., 10 (1959), 290–301. doi: 10.1093/jxb/10.2.290
[27] L. Preziosi, Cancer modelling and simulation, Chap. Hall/CRC, 2003.
[28] J. A. Spratt, D. A Fournier, J. S. Spratt, E. E. Weber, Decelerating growth and human breast cancer. Cancer, 71 (1993), 2013–2019.
[29] D. Bufnea, V. Niculescu, G. Silaghi, A. Sterca, Babeş-Bolyai University’s High Performance Computing Center, Stud. Univ. Babeş-Bolyai, Inf., 61 (2016), 54–69.
[30] E. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, Tata McGraw-Hill, New Delhi, 1972.
[31] D. Kaplan, L. Glass, Understanding Nonlinear Dynamics, Springer, New York, 1995.
[32] G. Lillacci, M. Khammash, Parameter estimation and model selection in computational biology, PLoS Comput. Biol., 6 (2010), 1000696. doi: 10.1371/journal.pcbi.1000696
[33] M. Quach, N. Brunel, F. d’Alché-Buc, Estimating parameters and hidden variables in non-linear state-space models based on ODEs for biological networks inference, Bioinformatics, 23 (2007), 3209–3216. doi: 10.1093/bioinformatics/btm510
[34] A. Tarantola, Inverse problem theory and methods for model parameter pstimation, SIAM, 2005.
[35] M. P. Gamcsik, K. K. Millis, O. M. Colvin, Noninvasive detection of elevated glutathione levels in MCF-7 cells resistant to 4-hydroperoxycyclophosphamide, Cancer Res., 55 (1995), 2012–2016.
[36] R. N. Buick, Cellular basis of chemotherapy in cancer chemotherapy handbook, Appl. Lange, (1994), 9.
[37] L. E. Keshet, Mathematical models in biology, Soc. Ind. Appl. Math., 2005.
