Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 73, Issue 8, Pages 1695-1733Publisher
SPRINGER
DOI: 10.1007/s11538-010-9586-4
Keywords
Travelling wave; Velocity jump process; Chemotaxis
Categories
Funding
- Mathematical Biosciences Institute under the US NSF [0635561]
- Mathematical Biosciences Institute
- BBSRC [BB/D019621/1]
- Ministry of Education, Science, and Technology [2009-0094068]
- European Research Council under the European Community [FP7/2007-2013, 239870]
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- Somerville College, University of Oxford
- BBSRC [BB/D019621/1] Funding Source: UKRI
- Biotechnology and Biological Sciences Research Council [BB/D019621/1] Funding Source: researchfish
- National Research Foundation of Korea [2009-0094068] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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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.
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