TRAVELLING WAVES IN HYBRID CHEMOTAXIS MODELS
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Abstract
Hybrid models of chemotaxis combine agent-based models of cells with partial differential
equation models of extracellular chemical signals. In this paper, travelling wave properties of
hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agentbased (individualbased) approach with internal dynamics describing signal transduction. In
addition to the chemotactic behaviour of the bacteria, the individual-based model also
includes cell proliferation and death. Cells consume the extracellular nutrient field
(chemoattractant) which is modelled using a partial differential equation. Mesoscopic and
macroscopic equations representing the behaviour of the hybrid model are derived and the
existence of travelling wave solutions for these models is established. It is shown that cell
proliferation is necessary for the existence of non-transient (stationary) travelling waves in
hybrid models. Additionally, a numerical comparison between the wave speeds of the
continuum models and the hybrid models shows good agreement in the case of weak
chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell
adaptation, we detect oscillating behaviour of the wave, which cannot be explained by meanfield approximations.
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