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An investigation on Monod–Haldane immune response based tumor-effector–interleukin-2 interactions with treatments

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  • Das, Parthasakha
  • Das, Pritha
  • Das, Samhita

Abstract

In this article, a mathematical model with time delay describing tumor immune interaction with Monod–Haldane kinetic response is proposed to reveal the dynamics of related inter-cellular phenomena. Positivity of the solutions, boundedness and uniform persistence of the system are determined to ensure the well-posedness of the system. The local stability of equilibria is studied as well as the length of the delay to preserve the stability is estimated for providing the mechanism of action to control the oscillation in tumor growth. Transcritical bifurcation using Sotomayer’s theorem and Hopf bifurcation are investigated analytically and numerically. Global stability is examined before the commencement of sustained oscillations using a suitable Lyapunov function. To observe the influence of tumor growth due to uncertainty in input parameters, Latin hypercube sampling based uncertainty analysis is performed followed by sensitivity analysis. Computer simulation results are illustrated to elucidate the change of dynamical behavior due to the change of system parameters.

Suggested Citation

  • Das, Parthasakha & Das, Pritha & Das, Samhita, 2019. "An investigation on Monod–Haldane immune response based tumor-effector–interleukin-2 interactions with treatments," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 536-551.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:536-551
    DOI: 10.1016/j.amc.2019.05.032
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    1. Kabir, K.M. Ariful & Tanimoto, Jun, 2019. "Dynamical behaviors for vaccination can suppress infectious disease – A game theoretical approach," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 229-239.
    2. Kabir, K.M. Ariful & Kuga, Kazuki & Tanimoto, Jun, 2019. "Analysis of SIR epidemic model with information spreading of awareness," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 118-125.
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    Cited by:

    1. Roy, Jyotirmoy & Alam, Shariful, 2020. "Fear factor in a prey–predator system in deterministic and stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    2. 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).

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