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Stochastic resonance in a tumor–immune system subject to bounded noises and time delay

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  • Guo, Wei
  • Mei, Dong-Cheng

Abstract

Immunotherapy is one of the most recent approaches in cancer therapy. A mathematical model of tumor–immune interaction, subject to a periodic immunotherapy treatment (imitated by a periodic signal), correlative and bounded stochastic fluctuations and time delays, is investigated by numerical simulations for its signal power amplification (SPA). Within the tailored parameter regime, the synchronous response of tumor growth to the immunotherapy, stochastic resonance (SR), versus both the noises and delays is obtained. The details are as follows (i) the peak values of SPA versus the noise intensity (A) in the proliferation term of tumor cells decrease as the frequency of periodic signal increases, i.e. an increase of the frequency restrains the SR; (ii) an increase of the amplitude of periodic signal restrains the SR versus A, but boosts up the SR versus the noise intensity B in the immune term; (iii) there is an optimum cross-correlated degree between the two bounded noises, at which the system exhibits the strongest SR versus the delay time τα(the reaction time of tumor cell population to their surrounding environment constraints); (iv) upon increasing the delay time τα, double SR versus the delay time τβ (the time taken by both the tumor antigen identification and tumor-stimulated proliferation of effectors) emerges. These results may be helpful for an immunotherapy treatment for the sufferer.

Suggested Citation

  • Guo, Wei & Mei, Dong-Cheng, 2014. "Stochastic resonance in a tumor–immune system subject to bounded noises and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 90-98.
    • Handle: RePEc:eee:phsmap:v:416:y:2014:i:c:p:90-98
    DOI: 10.1016/j.physa.2014.08.003
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    Citations

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    Cited by:

    1. Shi, Peiming & Xia, Haifeng & Han, Dongying & Fu, Rongrong & Yuan, Danzhen, 2018. "Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 8-14.
    2. Han, Ping & Xu, Wei & Zhang, Hongxia & Wang, Liang, 2022. "Most probable trajectories in the delayed tumor growth model excited by a multiplicative non-Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Guo, Qin & Sun, Zhongkui & Xu, Wei, 2016. "The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 43-52.
    4. Zhu, Ping, 2021. "An equivalent analytical method to deal with cross-correlated exponential type noises in the nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Hua, Mengjiao & Wu, Yu, 2022. "Transition and basin stability in a stochastic tumor growth model with immunization," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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