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Modelling and analysis of delayed tumour–immune system with hunting T-cells

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  • Dehingia, Kaushik
  • Das, Parthasakha
  • Upadhyay, Ranjit Kumar
  • Misra, Arvind Kumar
  • Rihan, Fathalla A.
  • Hosseini, Kamyar

Abstract

This study proposes a modified prey–predator-like model consisting of tumour cells, hunting T-cells, and resting T-cells to illustrate tumour–immune interaction by incorporating discrete-time-delay with conversion or growth of hunting cells. For analysis, the proposed system has been transformed into a normalized system, and its non-negativity solution has been verified. The linear stability of the system has been analysed at each equilibrium. The discrete-time delay affects the system’s stability, and the system undergoes a Hopf bifurcation. Moreover, the length of time delay for which a periodic solution can be preserved has been derived. Finally, numerical computations have been presented that correlate with analytical results and are also relevant from a biological perspective.

Suggested Citation

  • Dehingia, Kaushik & Das, Parthasakha & Upadhyay, Ranjit Kumar & Misra, Arvind Kumar & Rihan, Fathalla A. & Hosseini, Kamyar, 2023. "Modelling and analysis of delayed tumour–immune system with hunting T-cells," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 669-684.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:669-684
    DOI: 10.1016/j.matcom.2022.07.009
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    References listed on IDEAS

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    6. Liu, Peng & Liu, Xijun, 2017. "Dynamics of a tumor-immune model considering targeted chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 7-13.
    7. Das, Parthasakha & Das, Samhita & Das, Pritha & Rihan, Fathalla A. & Uzuntarla, Muhammet & Ghosh, Dibakar, 2021. "Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. Dong, Yueping & Huang, Gang & Miyazaki, Rinko & Takeuchi, Yasuhiro, 2015. "Dynamics in a tumor immune system with time delays," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 99-113.
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