Abstract
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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