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Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy

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  • Yang, Huan
  • Tan, Yuanshun
  • Yang, Jin
  • Liu, Zijian

Abstract

In this paper, a tumor-immune system with impulse comprehensive therapy and stochastic perturbation is investigated. The combination of pulsed chemotherapy and pulsed immunotherapy and the effect of environmental random disturbance are reflected in this model. The existence and uniqueness of global positive solution of the system are proved. It is determined that the expectation of the solution is always less than a constant by utilizing the comparison theorems of impulsive differential equations and that the tumor cells will become weakly persistent in the mean or extinct under some sufficient conditions. Our results and numerical simulations show that random disturbance can inhibit the growth of tumor cells, and the combination of chemotherapy and immunotherapy can reduce the damage of therapy to the healthy cells.

Suggested Citation

  • Yang, Huan & Tan, Yuanshun & Yang, Jin & Liu, Zijian, 2021. "Extinction and persistence of a tumor-immune model with white noise and pulsed comprehensive therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 456-470.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:456-470
    DOI: 10.1016/j.matcom.2020.11.014
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    References listed on IDEAS

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    1. Yang, Jin & Tang, Sanyi & Cheke, Robert A., 2015. "Modelling pulsed immunotherapy of tumour–immune interaction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 109(C), pages 92-112.
    2. Meng Liu, 2013. "Analysis of Stochastic Delay Predator-Prey System with Impulsive Toxicant Input in Polluted Environments," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, October.
    3. Guodong Liu & Xiaohong Wang & Xinzhu Meng & Shujing Gao, 2017. "Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps," Complexity, Hindawi, vol. 2017, pages 1-15, June.
    4. Yang, Jin & Tan, Yuanshun & Cheke, Robert A., 2019. "Modelling effects of a chemotherapeutic dose response on a stochastic tumour-immune model," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 1-13.
    5. Li, Dagen & Liu, Meng, 2020. "Invariant measure of a stochastic food-limited population model with regime switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 16-26.
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    Cited by:

    1. Shireen Jawad & Matthias Winter & Zain-Aldeen S. A. Rahman & Yasir I. A. Al-Yasir & Anwar Zeb, 2023. "Dynamical Behavior of a Cancer Growth Model with Chemotherapy and Boosting of the Immune System," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    2. Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.

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