Complex dynamics of a tumor-immune system with antigenicity

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.

• Publication year

  2021

• Venue

  Applied Mathematics and Computation

• Publication date

  2021-07-01

• Fields of study

  Biology, Physics, Computer Science, Mathematics, Medicine

• Identifiers
  DOI 10.1016/j.amc.2021.126052
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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