Traveling bands for the Keller-Segel model with population growth

Shangbing Ai, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.
Original languageEnglish
Pages (from-to)717-737
Number of pages21
JournalMathematical Biosciences and Engineering
Issue number4
Publication statusPublished - 1 Jan 2015


  • Cell kinetics
  • Chemotaxis
  • Keller-Segel model
  • Minimal wave speed
  • Traveling waves

ASJC Scopus subject areas

  • Modelling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics


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