The stability of tumor-immune system with time delay

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O175?? ????????

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    Objective The tumor-immune system reflects the complex dynamics underlying the interaction between tumor cells and immune cells. The stability of the deterministic tumor-immune system with time delay is researched by means of linear stability analysis method in this paper. Methods In view of time delay in the tumor-immune system since it takes some time for immune cells to recognize tumor cells to make appropriate responses, then the model is simplified by means of Taylor expansion of small delay, and the equilibria are solved out. By linear stability analysis method, the stability of these equilidria are studied. Results There are a stable focus, a stable node, and two saddles in system. Moreover, the type and stability of these equilibria are not affected by the delay. Conclusions Numerical simulation demonstrates previous conclusions. The results can help to have a deep understanding of the dynamics mechanisms of tumor immune response and provide a reference for tumor growth and treatment.

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  • Received:April 26,2022
  • Revised:June 13,2022
  • Adopted:June 16,2022
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