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Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach

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  • Das, Parthasakha
  • Das, Samhita
  • Upadhyay, Ranjit Kumar
  • Das, Pritha

Abstract

In this article, we propose and analyze an optimal control problem of a delayed tumor-immune model in presence of a multi immuno-chemotherapeutic drug. Local dynamics of drug-free steady states are studied and Hopf-bifurcation is observed with delay bifurcation parameter. By formulating a quadratic control based functional, an optimal control problem is constructed with treatments as control variables. The formulation of the functional is aimed at minimizing the proliferation rate of tumor cells and the detrimental effects of injected drugs. Additionally, maximizing the effector cells and maintaining an attributed level of normal cells are also a priority. By applying Pontryagin’s maximum principle, the sufficient and necessary conditions of optimality system are established. The sensitivity analysis of cost functional is performed with different combinations of control variables. The cost-effectiveness analysis is carried out to determine the most cost-effective strategy. The numerical results verify analytical findings and demonstrate that a multi-therapeutic treatment protocol can alleviate tumor burden within a few months of drug administration.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302071
    DOI: 10.1016/j.chaos.2020.109806
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    1. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    2. Rihan, F.A. & Velmurugan, G., 2020. "Dynamics of fractional-order delay differential model for tumor-immune system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Andreas Diefenbach & Eric R. Jensen & Amanda M. Jamieson & David H. Raulet, 2001. "Rae1 and H60 ligands of the NKG2D receptor stimulate tumour immunity," Nature, Nature, vol. 413(6852), pages 165-171, September.
    4. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    5. El-Gohary, Awad, 2008. "Chaos and optimal control of cancer self-remission and tumor system steady states," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1305-1316.
    6. 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.
    7. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar & Samanta, G.P., 2016. "Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 111-122.
    8. El-Gohary, Awad & Alwasel, I.A., 2009. "The chaos and optimal control of cancer model with complete unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2865-2874.
    9. Das, Parthasakha & Mukherjee, Sayan & Das, Pritha, 2019. "An investigation on Michaelis - Menten kinetics based complex dynamics of tumor - immune interaction," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 297-305.
    10. Datta, Jyotiska & Jana, Debaldev & Upadhyay, Ranjit Kumar, 2019. "Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 229-235.
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    1. 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.
    2. 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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