Original Article | Open Access
C. F. Lo, "A Modified Stochastic Gompertz Model for Tumour Cell Growth", Computational and Mathematical Methods in Medicine, vol. 11, Article ID 765839, 9 pages, 2010. https://doi.org/10.1080/17486700802545543
A Modified Stochastic Gompertz Model for Tumour Cell Growth
Based 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.
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