Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The invasion speed of cell migration models with realistic cell cycle
  time distributions   Cell proliferation is typically incorporated into stochastic mathematical
models of cell migration by assuming that cell divisions occur after an
exponentially distributed waiting time. Experimental observations, however,
show that this assumption is often far from the real cell cycle time
distribution (CCTD). Recent studies have suggested an alternative approach to
modelling cell proliferation based on a multi-stage representation of the CCTD.
In order to validate and parametrise these models, it is important to connect
them to experimentally measurable quantities. In this paper we investigate the
connection between the CCTD and the speed of the collective invasion. We first
state a result for a general CCTD, which allows the computation of the invasion
speed using the Laplace transform of the CCTD. We use this to deduce the range
of speeds for the general case. We then focus on the more realistic case of
multi-stage models, using both a stochastic agent-based model and a set of
reaction-diffusion equations for the cells' average density. By studying the
corresponding travelling wave solutions, we obtain an analytical expression for
the speed of invasion for a general N-stage model with identical transition
rates, in which case the resulting cell cycle times are Erlang distributed. We
show that, for a general N-stage model, the Erlang distribution and the
exponential distribution lead to the minimum and maximum invasion speed,
respectively. This result allows us to determine the range of possible invasion
speeds in terms of the average proliferation time for any multi-stage model.

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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: astro-ph