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Analysis of a hybrid impulsive tumor-immune model with immunotherapy and chemotherapy

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  • Zhao, Zhong
  • Pang, Liuyong
  • Li, Qiuying

Abstract

In this paper, a tumour-immune model with pulsed treatment of different frequency is proposed. The globally attractive conditions of the tumour-free periodic solution are presented in views of the comparison theorem for impulsive differential equations. Furthermore, the effect of period, dosage and times of drug delivery on the critical threshold is addressed by means of computer simulation, which indicates that there exists an optimal frequency of chemotherapeutic application. In addition, a tumour-immune model with fixed-time pulsed of immunotherapy and state feedback impulsive chemotherapy is given to keep the normal cells above and toxicity below the acceptable levels. Some numerical results are also provided to investigate the effect of the initial densities, predetermined threshold, drug dose and impulsive period on the dynamical behavior of hybrid impulsive system.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077920310080
    DOI: 10.1016/j.chaos.2020.110617
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    References listed on IDEAS

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    1. Liu, Zijian & Yang, Chenxue, 2016. "A mathematical model of cancer treatment by radiotherapy followed by chemotherapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 1-15.
    2. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    3. Khajanchi, Subhas & Nieto, Juan J., 2019. "Mathematical modeling of tumor-immune competitive system, considering the role of time delay," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 180-205.
    4. Yu, Jui-Ling & Jang, Sophia R.-J., 2019. "A mathematical model of tumor-immune interactions with an immune checkpoint inhibitor," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    5. 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).
    6. 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.
    7. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    8. 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.
    9. 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.
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