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An investigation on Michaelis - Menten kinetics based complex dynamics of tumor - immune interaction

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  • Das, Parthasakha
  • Mukherjee, Sayan
  • Das, Pritha

Abstract

We investigate the dynamics of a three-dimensional tumor-immune interactions system. Local dynamics of the system has studied by the finding stability and Hopf bifurcation at biologically feasible equilibria. Further, chaotic phenomena have been investigated by measuring the asymptotic growth of the corresponding phase space trajectory with the various bifurcating parameters of the system. A dynamics of mean fluctuations of the tumor growth based on its local maxima have investigated under the same parameters. A significant correlation between the fluctuations and the tumor dynamics have verified by statistical analysis.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:297-305
    DOI: 10.1016/j.chaos.2019.08.006
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    1. Abernethy, Sam & Gooding, Robert J., 2018. "The importance of chaotic attractors in modelling tumour growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 268-277.
    2. Mukherjee, Sayan & Palit, Sanjay Kumar & Banerjee, Santo & Wahab, A.W.A. & Ariffin, MRK & Bhattacharya, D.K., 2017. "Computing two dimensional Poincaré maps for hyperchaotic dynamics," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 140-154.
    3. Catherine M. Koebel & William Vermi & Jeremy B. Swann & Nadeen Zerafa & Scott J. Rodig & Lloyd J. Old & Mark J. Smyth & Robert D. Schreiber, 2007. "Adaptive immunity maintains occult cancer in an equilibrium state," Nature, Nature, vol. 450(7171), pages 903-907, December.
    4. He, Shaobo & Fataf, N.A.A. & Banerjee, Santo & Sun, Kehui, 2019. "Complexity in the muscular blood vessel model with variable fractional derivative and external disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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    Cited by:

    1. 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).
    2. 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).
    3. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    5. Konstantin E. Starkov & Alexander P. Krishchenko, 2024. "On the Dynamics of Immune-Tumor Conjugates in a Four-Dimensional Tumor Model," Mathematics, MDPI, vol. 12(6), pages 1-16, March.
    6. 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.
    7. 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).
    8. Kemwoue, Florent Feudjio & Deli, Vandi & Edima, Hélène Carole & Mendimi, Joseph Marie & Gninzanlong, Carlos Lawrence & Dedzo, Mireille Mbou & Tagne, Jules Fossi & Atangana, Jacques, 2022. "Effects of delay in a biological environment subject to tumor dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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