Stochastic Nonlinear Gompertz Model of （随机非线性龚帕兹模型）.pdf

Proceedings of the World Congress on Engineering 2009 Vol II WCE 2009, July 1 - 3, 2009, London, U.K. Stochastic Nonlinear Gompertz Model of Tumour Growth C.F. Lo∗ Abstract differential equation: In this communication, based upon the deterministic dx= {A x−A xln (x)} dt , (1) 1 2 Gompertz growth law, a stochastic nonlinear model of tumour growth is proposed to model the conventional where A1 is the intrinsic growth rate of the tumour size-dependent therapy strategy of tumours. The (related to the initial mitosis rate) and A2 is the probability density function of the size of the tumour growth deceleration factor (related to the antiangio- obeys a nonlinear Fokker-Planck equation which can genic processes). The parameters A and A charac- 1 2 be solved analytically. It is found that during the terize the evolution of different tumour types. Eq.(1) cancer treatments the dose intensity should not be admits the solution of the form of a sigmoidal func- decreased at any time because this will allow the tu- tion: ½ · ¸ ¾ mour to relapse, and that the late logarithmic inten- A1 A1 sification therapy could be the optimal therapeutic