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Dynamics of fractional-order delay differential model for tumor-immune system

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  • Rihan, F.A.
  • Velmurugan, G.

Abstract

Time-delays and fractional-order play a vital role in modeling biological systems with memory. In this paper, we propose a novel delay differential model with fractional-order for tumor immune system with external treatments. Non-negativity of the solution of such model has been investigated. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to two differenttumor time-delays τ1 and τ2. The occurrence of Hopf bifurcation is captured when any of the time-delay passes through critical value τ1*, or τ2*. Theoretical results are validated numerically by solving the governing system, using the modified Adams–Bashforth–Moulton predictor-corrector scheme. Our findings show that the combination of fractional-order derivative and time-delay in the model improves the dynamics and increases complexity of the model.

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  • Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305491
    DOI: 10.1016/j.chaos.2019.109592
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    Cited by:

    1. Xu, Changjin & Farman, Muhammad & Akgül, Ali & Nisar, Kottakkaran Sooppy & Ahmad, Aqeel, 2022. "Modeling and analysis fractal order cancer model with effects of chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Ndenda, J.P. & Njagarah, J.B.H. & Shaw, S., 2021. "Role of immunotherapy in tumor-immune interaction: Perspectives from fractional-order modelling and sensitivity analysis," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Das, Parthasakha & Das, Samhita & Upadhyay, Ranjit Kumar & Das, Pritha, 2020. "Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    5. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    6. Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    7. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. 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).

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