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

doi:10.1016/j.matcom.2022.07.009

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	669-684
Number of pages	16
Journal	Mathematics and Computers in Simulation
Volume	203
DOIs	https://doi.org/10.1016/j.matcom.2022.07.009
Publication status	Published - Jan 2023

Keywords

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

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)
Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.matcom.2022.07.009

Cite this

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title = "Modelling and analysis of delayed tumour–immune system with hunting T-cells",

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.",

keywords = "Hopf-bifurcation, Hunting T-cells, Time-delay, Tumour–immune interaction",

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AU - Dehingia, Kaushik

AU - Das, Parthasakha

AU - Upadhyay, Ranjit Kumar

AU - Misra, Arvind Kumar

AU - Rihan, Fathalla A.

AU - Hosseini, Kamyar

PY - 2023/1

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N2 - 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.

AB - 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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