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Research Article

Dynamical behaviour of a tumour-immune model focusing on the dosage of targeted chemotherapeutic drug

ORCID Icon, ORCID Icon & ORCID Icon
Pages 2568-2582 | Received 19 Feb 2019, Accepted 18 Apr 2022, Published online: 18 May 2022

References

  • L. de Pillis, W. Gu, and A. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modelling, applications and biological interpretations, J. Theoret. Biol. 238(4) (2006), pp. 841–862.
  • L.G. de Pillis and A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: An optimal control approach, Comput. Math. Methods Med. 3(2) (2001), pp. 79–100.
  • 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(17) (2005), pp. 7950–7958.
  • B. Dhar and P. Gupta, Numerical solution of tumor-immune model including small molecule drug by multi-step differential transform method, Int. J. Adv. Trends Comput. Sci. Eng. 8(5) (2019), pp. 1802–1807.
  • B. Dhar and P.K Gupta, Mathematical analysis on the behaviour of tumor cells in the presence of monoclonal antibodies drug, in Modeling, Simulation and Optimization: Proceedings of CoMSO 2020, Springer, Singapore, 2021, pp. 311–321.
  • B. Dhar and P.K. Gupta, A numerical approach of tumor-immune model with B cells and monoclonal antibody drug by multi-step differential transformation method, Math. Methods Appl. Sci. 44(5) (2021), pp. 4058–4070.
  • R. Ganguly and I. Puri, Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis, Cell Prolif 40 (2006), pp. 338–354.
  • D. Ghosh, S. Khajanchi, S. Mangiarotti, F. Denis, S.K. Dana, and C. Letellier, How tumor growth can be influenced by delayed interactions between cancer cells and the microenvironment, Biosystems158 (2017), pp. 17–30.
  • P. Gupta and B. Dhar, Dynamical behaviour of fractional order tumor-immune model with targeted chemotherapy treatment, Int. J. Eng. Technol. 7(2.28) (2018), pp. 6–9.
  • D. Kirschner and J.C. Panetta, Modeling immunotherapy of the tumor–immune interaction, J. Math. Biol. 37(3) (1998), pp. 235–252.
  • V. Kuznetsov and A. Perelson, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull. Math. Biol. 56(4) (1994), pp. 295–321.
  • K.L. Liao, X.F. Bai, and A. Friedman, Mathematical modeling of interleukin-27 induction of anti-tumor t cells response, PLoS ONE 9(3) (2014), pp. e91844.
  • X. Lin, X. Li, and X Lin, A review on applications of computational methods in drug screening and design, Molecules 25(6) (2020), pp. 1375.
  • P. Liu and X Liu, Dynamics of a tumor-immune model considering targeted chemotherapy, Chaos, Solitons & Fractals 98 (2017), pp. 7–13.
  • S. Sharma and G. Samanta, Dynamical behaviour of a tumor-immune system with chemotherapy and optimal control, J. Nonlinear Dynam.( 2013) 2013.
  • S. Sharma and G. Samanta, Analysis of the dynamics of a tumor–immune system with chemotherapy and immunotherapy and quadratic control, Differential Equations Dynam. Systems 24 (2) (2016), pp. 149–171.
  • The American Cancer Society Medical and Editorial Content Team. Benefits of good nutrition during cancer treatment, 2019.
  • P.A. Valle, K.E. Starkov, and L.N Coria, Global stability and tumor clearance conditions for a cancer chemotherapy system, Commun. Nonlinear Sci. Numer. Simul. 40 (2016), pp. 206–215.
  • R. Yafia, Hopf bifurcation in differential equations with delay for tumor–immune system competition model, SIAM J. Appl. Math. 67 (7)(2007), pp. 1693–1703.
  • A. Yousef, F. Bozkurt, and T. Abdeljawad, Mathematical modeling of the immune-chemotherapeutic treatment of breast cancer under some control parameters, Adv. Difference Equ. 2020 1 (2020), pp. 1–25.
  • L. Zhong, Y. Li, L. Xiong, W. Wang, M. Wu, T. Yuan, W. Yang, C. Tian, Z. Miao, T. Wang, and S. Yang, Small molecules in targeted cancer therapy: Advances, challenges, and future perspectives, Signal Transduct Target Therapy 6 (1)(2021), pp. 1–48.

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