A Cell Growth Model Revisited
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 sati...
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| Format: | Journal article |
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2009
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| _version_ | 1826280520119484416 |
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| author | Derfel, G van Brunt, B Wake, G |
| author_facet | Derfel, G van Brunt, B Wake, G |
| author_sort | Derfel, G |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:14:56Z |
| format | Journal article |
| id | oxford-uuid:7a7c7ec7-dc5b-421b-a738-9897ce15fbac |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:14:56Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:7a7c7ec7-dc5b-421b-a738-9897ce15fbac2022-03-26T20:44:24ZA Cell Growth Model RevisitedJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7a7c7ec7-dc5b-421b-a738-9897ce15fbacMathematical Institute - ePrints2009Derfel, Gvan Brunt, BWake, G 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. |
| spellingShingle | Derfel, G van Brunt, B Wake, G A Cell Growth Model Revisited |
| title | A Cell Growth Model Revisited |
| title_full | A Cell Growth Model Revisited |
| title_fullStr | A Cell Growth Model Revisited |
| title_full_unstemmed | A Cell Growth Model Revisited |
| title_short | A Cell Growth Model Revisited |
| title_sort | cell growth model revisited |
| work_keys_str_mv | AT derfelg acellgrowthmodelrevisited AT vanbruntb acellgrowthmodelrevisited AT wakeg acellgrowthmodelrevisited AT derfelg cellgrowthmodelrevisited AT vanbruntb cellgrowthmodelrevisited AT wakeg cellgrowthmodelrevisited |