Article thumbnail
Location of Repository

A Cell Growth Model Revisited

By G Derfel, B van Brunt and Graeme Wake


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:

Suggested articles


  1. (1989). A functional differential equation arising in the modelling of cell-growth”, doi
  2. (1964). An absorption probablility problem”,
  3. (2004). Modelling Cell Death in Human Tumour Cell Lines Exposed to the Anticancer Drug Paclitaxel”, doi
  4. (1944). On the fluctuation of the brightness of the Milky Way”,
  5. (1993). On the generalized pantograph functional differential equation”, doi
  6. (1989). Probabilistic method for a class of functional differential equations”, doi
  7. Steady size distributions for cells in one dimensional plant tissues”, doi
  8. (1955). The Convolution Transform,
  9. (1971). The functional-differential equation y′(x)

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.