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A Cell Growth Model Revisited

By G Derfel, B van Brunt and Graeme Wake

Abstract

In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This shows that the functional differential equation which describes the steady form of the steady-size distribution which is approached asymptotically and satisfies the well-known pantograph equation is more simply derived via a Poisson process. This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework

Topics: Partial differential equations
Year: 2009
OAI identifier: oai:generic.eprints.org:824/core69

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Citations

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