Dynamics of a model of tumor-immune interaction with time delay and noise

Lifeng Han, Changhan He, Yang Kuang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We propose a model of tumor-immune interaction with time delay in immune reaction and noise in tumor cell reproduction. Immune response is modeled as a non-monotonic function of tumor burden, for which the tumor is immunogenic at nascent stage but starts inhibiting immune system as it grows large. Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and uncertainty in the tumor innate proliferation rate are studied by including delay and noise in the appropriate model terms. Stability, persistence and extinction of the tumor are analyzed. We find that delay and noise can both induce the transition from low tumor burden equilibrium to high tumor equilibrium. Moreover, our result suggests that the elimination of cancer depends on the basal level of the immune system rather than on its response speed to tumor growth.

Original languageEnglish (US)
Pages (from-to)2347-2363
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number9
StatePublished - Sep 2020


  • And phrases. Time delay
  • Persistence
  • Stability
  • Stochasticity
  • Tumor-immune interaction

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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