A modified stochastic Gompertz model for tumour cell growth
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AbstractBased upon the deterministic Gompertz law of cell growth, we have proposed a stochastic model of tumour cell growth, in which the size of the tumour cells is bounded. The model takes account of both cell fission (which is an 'action at a distance' effect) and mortality too. Accordingly, the density function of the size of the tumour cells obeys a functional Fokker-Planck Equation (FPE) associated with the bounded stochastic process. We apply the Lie-algebraic method to derive the exact analytical solution via an iterative approach. It is found that the density function exhibits an interesting kink-like structure generated by cell fission as time evolves.
All Author(s) ListLo CF
Journal nameComputational and Mathematical Methods in Medicine
Year2010
Month1
Day1
Volume Number11
Issue Number1
PublisherTaylor & Francis: STM, Behavioural Science and Public Health Titles / Hindawi Publishing Corporation
Pages3 - 11
ISSN1748-670X
eISSN1748-6718
LanguagesEnglish-United Kingdom
Keywordsbounded random process; Fokker-Planck equation; Lie-algebraic method
Web of Science Subject CategoriesMathematical & Computational Biology; MATHEMATICAL & COMPUTATIONAL BIOLOGY

Last updated on 2020-20-10 at 00:39