Asymmetric non-Gaussian effects in a tumor growth model with immunization

Mengli Hao, Jinqiao Duan, Renming Song, Wei Xu

Research output: Contribution to journalArticle


The dynamical evolution of a tumor growth model, under immune surveillance and subject to asymmetric non-Gaussian α-stable Lévy noise, is explored. The lifetime of a tumor staying in the range between the tumor-free state and the stable tumor state, and the likelihood of noise-induced tumor extinction, are characterized by the mean residence time and the escape probability, respectively. For various initial densities of tumor cells, the mean residence time and the escape probability are computed with different noise parameters. It is observed that unlike the Gaussian noise or symmetric non-Gaussian noise, the asymmetric non-Gaussian noise plays a constructive role in the tumor evolution in this simple model. By adjusting the noise parameters, the mean residence time can be shortened and the escape probability can be increased, simultaneously. This suggests that a tumor may be mitigated with higher probability in a shorter time, under certain external environmental stimuli.

Original languageEnglish (US)
Pages (from-to)4428-4444
Number of pages17
JournalApplied Mathematical Modelling
Issue number17-18
StatePublished - Sep 1 2014


  • Asymmetric α-stable Lévy motion
  • Escape probability
  • Lévy jump measure
  • Mean residence time
  • Stochastic dynamics of tumor growth
  • Tumor growth with immunization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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