We study the effect of noise in an avascular tumor growth model. The growth mechanism we consider is the Gompertz model. The steady state probability distributions and average population of tumor cells are analyzed within the Fokker-Planck formalism to investigate the importance of additive and multiplicative noise. We consider the effect of correlation on tumor growth for both the case of nonzero and zero correlation time. It is observed that the Gompertz model, driven by correlated noise exhibits a stochastic resonance and phase transition. This behaviour is attributed to multiplicative noise. In the case of nonzero correlation time, it is found that the correlation strength and correlation time have opposite effects on the steady state probability distribution. The Gompertz model simulations are also shown to be in qualitative agreement with another similiar non-bistable system, the logistic model.
Fluctuation phenomena; Random processes; Noise; Brownian motion
