MBI Publications

MBI Publications for Radek Erban (5)

  • R. Erban, H. hwang, K. Painter and C. Xue
    Traveling waves in bacteria chemotaxis
    (In Preparation)

    Abstract

  • C. Xue, H. Othmer and R. Erban
    From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems, Multiscale Phenomena in Biology
    Proceedings of the 2nd Okinawa Conference on Mathematics and Biology, AIPVol. 1167 (2009) pp. 3-14

    Abstract

  • C. Xue, H. Othmer and R. Erban
    From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems
    Multiscale Phenomena in Biology: Proceedings of the 2nd Okinawa Conference on Mathematics and Biology, AIPVol. 1167 (2009) pp. 3-14

    Abstract

  • C. Xue, H. hwang, K. Painter and R. Erban
    Traveling waves in bacterial chemotaxis
    Bul. Math. Biol (2011)

    Abstract

    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.
  • C. Xue, H. hwang, K. Painter and R. Erban
    Traveling waves in hyperbolic chemotaxis equations
    Bul. Math. BiolVol. 73 No. 8 (2012) pp. 1695-1733

    Abstract

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