Exact representations for tumour incidence for some density-dependent models
Carcinogenesis is a multistage random process involving generic changes and stochastic proliferation and differentiation of normal cells and genetically altered stem cells. In this paper, we present the probability of time to tumour onset for a carcinogenesis model wherein the cells grow according...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2655 |
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| author | P. R. Parthasarathy Klaus Dietz |
| author_facet | P. R. Parthasarathy Klaus Dietz |
| author_sort | P. R. Parthasarathy |
| collection | DOAJ |
| description | Carcinogenesis is a multistage random process involving generic
changes and stochastic proliferation and differentiation of normal
cells and genetically altered stem cells. In this paper, we
present the probability of time to tumour onset for a
carcinogenesis model wherein the cells grow according to a
birth and death process with density-dependent birth and death
rates. This is achieved by transforming the underlying system of
difference equations which results in a continued fraction. This
continued fraction approach helps us to find the complete
solutions. The popular Moolgavkar-Venzon-Knudson (MVK)
model assumes constant birth, death, and transition rates. |
| format | Article |
| id | doaj-art-eb9f44bbdf364f1fb11236931909c87c |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-eb9f44bbdf364f1fb11236931909c87c2025-08-20T03:21:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005162655266710.1155/IJMMS.2005.2655Exact representations for tumour incidence for some density-dependent modelsP. R. Parthasarathy0Klaus Dietz1Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600036, IndiaDepartment of Medical Biometry, University of Tuebingen, Tuebingen 72070, GermanyCarcinogenesis is a multistage random process involving generic changes and stochastic proliferation and differentiation of normal cells and genetically altered stem cells. In this paper, we present the probability of time to tumour onset for a carcinogenesis model wherein the cells grow according to a birth and death process with density-dependent birth and death rates. This is achieved by transforming the underlying system of difference equations which results in a continued fraction. This continued fraction approach helps us to find the complete solutions. The popular Moolgavkar-Venzon-Knudson (MVK) model assumes constant birth, death, and transition rates.http://dx.doi.org/10.1155/IJMMS.2005.2655 |
| spellingShingle | P. R. Parthasarathy Klaus Dietz Exact representations for tumour incidence for some density-dependent models International Journal of Mathematics and Mathematical Sciences |
| title | Exact representations for tumour incidence for some density-dependent models |
| title_full | Exact representations for tumour incidence for some density-dependent models |
| title_fullStr | Exact representations for tumour incidence for some density-dependent models |
| title_full_unstemmed | Exact representations for tumour incidence for some density-dependent models |
| title_short | Exact representations for tumour incidence for some density-dependent models |
| title_sort | exact representations for tumour incidence for some density dependent models |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2655 |
| work_keys_str_mv | AT prparthasarathy exactrepresentationsfortumourincidenceforsomedensitydependentmodels AT klausdietz exactrepresentationsfortumourincidenceforsomedensitydependentmodels |