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Optimal control of tumour-immune model with time-delay and immuno-chemotherapy

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  • Rihan, F.A.
  • Lakshmanan, S.
  • Maurer, H.

Abstract

Herein, we study an optimal control problem of delay differential model to describe the dynamics of tumour-immune interactions in presence of immuno-chemotherapy. The model includes constant delays in the mitotic phase to justify the time required to stimulate the effector cells and for the effector cells to develop a suitable response to the tumour cells. By applying optimal control theory, we seek to minimize the cost associated with the immuno-chemotherapy and to reduce load of of tumour cells. Non-Negativity of the solutions of the model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are also discussed. We numerically approximate the solution of the optimal control problem by solving the state system forward and adjoint system backward in time. The numerical simulations show that the combination of immuno-chemotherapy protocol reduces the tumour load in few months of therapy.

Suggested Citation

  • Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:147-165
    DOI: 10.1016/j.amc.2019.02.002
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    References listed on IDEAS

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    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.
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    Cited by:

    1. R. Rakkiyappan & V. Preethi Latha & Fathalla A. Rihan, 2019. "A Fractional-Order Model for Zika Virus Infection with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    2. Zhou, Haihua & Song, Huijuan & Wang, Zejia, 2022. "The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. 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).
    4. Zhao, Zhong & Pang, Liuyong & Li, Qiuying, 2021. "Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    6. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    7. Li, Shunjie & Zhang, Xuebing & An, Qi, 2024. "A rumor spreading multi-delay model with delay-dependent parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 34-49.
    8. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. 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).
    10. 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).
    11. M. P. Rajan & C. K. Nanditha, 2022. "A Multi-Drug Pharmacokinectic Optimal Control Approach in Cancer Chemotherapy," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 314-333, October.

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