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Analysis of noise-induced phenomena in the nonlinear tumor–immune system

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  • Bashkirtseva, I.
  • Ryashko, L.

Abstract

The effect of random disturbances on the corporate dynamics of immune and tumor cells is studied on the basis of the mathematical model proposed by Kuznetsov et al. This model possesses two equilibria corresponding to opposite regimes of ”tumor dormancy” and ”tumor explosion”. We study the system dynamics under the variation of the parameter of inactivation of immune cells by tumor cells. For deterministic model, parametric mono- and bistable zones and the corresponding changes in the basins of attraction are described. We investigate how the multiplicative random noise can change the dynamics of this tumor–immune system. Mechanisms of the noise-induced suppression and growth of tumor cells are investigated in detail. Furthermore, we reveal that near the saddle–node bifurcation points, the random disturbances can destroy the bistability and generate the intermittent oscillations between high and low levels of tumor cells. We perform an analysis of these phenomena by a novel approach based on the stochastic sensitivity functions and confidence domains.

Suggested Citation

  • Bashkirtseva, I. & Ryashko, L., 2020. "Analysis of noise-induced phenomena in the nonlinear tumor–immune system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    • Handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437119321764
    DOI: 10.1016/j.physa.2019.123923
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    References listed on IDEAS

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    1. Bashkirtseva, I.A & Ryashko, L.B, 2000. "Sensitivity analysis of the stochastically and periodically forced Brusselator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 126-139.
    2. Liu, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
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    Citations

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    Cited by:

    1. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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