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Complex dynamics of a tumor-immune system with antigenicity

Author

Listed:
  • Li, Jianquan
  • Xie, Xin
  • Chen, Yuming
  • Zhang, Dian

Abstract

With the effect of antigenicity in consideration, we propose and analyze a conceptual model for the tumor-immune interaction. The model is described by a system of two ordinary differential equations. Though simple, the model can have complicated dynamical behaviors. Besides the tumor-free equilibrium, there can be up to three tumor-present equilibria, which can be a saddle or stable node/focus. Sufficient conditions on the nonexistence of nonconstant periodic solutions are provided. Bifurcation analysis including Hopf bifurcation and Bogdanov–Takens bifurcation is carried out. The theoretical results are supported by numerical simulations. Numerical simulations reveal the complexity of the dynamical behaviors of the model, which includes the subcritical/supercritical Hopf bifurcation, homoclinic bifurcation, saddle-node bifurcation at a nonhyperbolic periodic orbit, the appearance of two limit cycles with a singular closed orbit, and so on. Some biological implications of the theoretical results and numerical simulations are also provided.

Suggested Citation

  • Li, Jianquan & Xie, Xin & Chen, Yuming & Zhang, Dian, 2021. "Complex dynamics of a tumor-immune system with antigenicity," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001004
    DOI: 10.1016/j.amc.2021.126052
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    References listed on IDEAS

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    1. Dong, Yueping & Huang, Gang & Miyazaki, Rinko & Takeuchi, Yasuhiro, 2015. "Dynamics in a tumor immune system with time delays," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 99-113.
    2. 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.
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    Cited by:

    1. Dong, Cunjuan & Xiang, Changcheng & Xiang, Zhongyi & Yang, Yi, 2022. "Global dynamics of a Filippov epidemic system with nonlinear thresholds," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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