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Modelling pulsed immunotherapy of tumour–immune interaction

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  • Yang, Jin
  • Tang, Sanyi
  • Cheke, Robert A.

Abstract

We develop a mathematical model that describes the tumour–immune interaction and the effect on it of pulsed immunotherapy, based on the administration of adoptive cellular immunotherapy (ACI) combined with interleukin-2 (IL-2). The stability conditions for the tumour-free periodic solution are provided with different frequencies of ACI applications and IL-2 infusions. Furthermore, the effects of period, dosage and times of drug deliveries on the amplitudes of the tumour-free periodic solution were investigated. The most feasible immunotherapy strategy was determined by comparing immunotherapy with ACI treatment with or without IL-2. However, to investigate how to enhance the efficacy of chemotherapy (radiotherapy) and reduce its side-effects, we developed a model involving periodic applications of immunotherapy with chemotherapy (radiotherapy) applied only when the density of the tumour reached a given threshold. The results revealed that the initial densities, the effector cell: tumour cell ratios, the periods T and a given critical number of tumour cells CT are crucial for cancer treatment, which confirms that it is important to customize treatment strategies for individual patients.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:109:y:2015:i:c:p:92-112
    DOI: 10.1016/j.matcom.2014.09.001
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    References listed on IDEAS

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    1. Steven A. Rosenberg, 2001. "Progress in human tumour immunology and immunotherapy," Nature, Nature, vol. 411(6835), pages 380-384, May.
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. Li, Qian & Xiao, Yanni, 2019. "Bifurcation analyses and hormetic effects of a discrete-time tumor model," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.

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