ArticleMathematical medicine and biology : a journal of the IMA2025
Oscillations in a tumor-immune system interaction model with immune response delay.
Article in Mathematical medicine and biology : a journal of the IMA, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Data-driven modeling of spatiotemporal dynamics using multimodal imaging data.PLoS computational biology · 2026Article
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5 authors.
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Abstract
In this paper we consider a tumor-immune system interaction model with immune response delay, in which a nonmonotonic function is used to describe immune response to the tumor burden and a time delay is used to represent the time for the immune system to respond and take effect. It is shown that the model may have one, two or three tumor equilibria, respectively, under different conditions. Time delay can only affect the stability of the low tumor equilibrium, and local Hopf bifurcation occurs when the time delay passes through a critical value. The direction and stability of the bifurcating periodic solutions are also determined. Moreover, the global existence of periodic solutions is established by using a global Hopf bifurcation theorem. We also observe the existence of relaxation oscillations and complex oscillating patterns driven by the time delay. Numerical simulations are presented to illustrate the theoretical results.
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