Travelling Waves in Hyperbolic Chemotaxis Equations

Chuan Xue*, Hyung Ju Hwang, Kevin J. Painter, Radek Erban

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.

Original languageEnglish
Pages (from-to)1695-1733
Number of pages39
JournalBulletin of Mathematical Biology
Issue number8
Publication statusPublished - Aug 2011


  • Chemotaxis
  • Travelling wave
  • Velocity jump process

ASJC Scopus subject areas

  • Neuroscience(all)
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Pharmacology
  • Immunology
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)


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