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Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions

Author

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  • F. A. Rihan
  • M. Safan
  • M. A. Abdeen
  • D. Abdel Rahman

Abstract

We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. We explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. The possibility of clearing the tumor, with a strategy, is based on two parameters in the model: the rate of influx of the effector cells and the rate of influx of IL-2. The critical tumor-growth rate, below which endemic tumor does not exist, has been found. One can use the model to make predictions about tumor dormancy.

Suggested Citation

  • F. A. Rihan & M. Safan & M. A. Abdeen & D. Abdel Rahman, 2012. "Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-19, February.
    • Handle: RePEc:hin:jnljam:475720
    DOI: 10.1155/2012/475720
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    Cited by:

    1. Rihan, F.A. & Abdel Rahman, D.H. & Lakshmanan, S. & Alkhajeh, A.S., 2014. "A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 606-623.
    2. 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.
    3. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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