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

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

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)669-684
Number of pages16
JournalMathematics and Computers in Simulation
Publication statusPublished - Jan 2023


  • Hopf-bifurcation
  • Hunting T-cells
  • Time-delay
  • Tumour–immune interaction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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