Comment on “Correlated noise in a logistic growth model”

Abstract

We argue that the results published by Ai [Phys. Rev. E 67, 022903 (2003)] on "correlated noise in logistic growth" are not correct. Their conclusion that, for larger values of the correlation parameter lambda , the cell population is peaked at x=0, which denotes a high extinction rate, is also incorrect. We find the reverse behavior to their results, that increasing lambda promotes the stable growth of tumor cells. In particular, their results for the steady-state probability, as a function of cell number, at different correlation strengths, presented in Figs. 1 and 2 of their paper show different behavior than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation that at small values of cell number the steady-state probability increases as the correlation parameter is increased is also questionable. Another striking feature in their Figs. 1 and 3 is that, for the same values of the parameters lambda and alpha, their simulation produces two different curves, both qualitatively and quantitatively.

The effect of correlated noise in a Gompertz tumor growth model

“…In other words the distribution of the cell population which was mainly peaked about zero (for smaller values of λ) signifies high extinction rates, and moves towards zero with the decrease of the correlation parameter λ. Similar behaviour has also been obtained in the case of logistic growth [19]. Comparing Figs.…”

“…It is worth mentioning here that in the logistic model we found our calculations significantly differed from those of both [9] and [10]. These results can be reproduced if one considers a negative correlation strength (λ) between additive and multiplicative noise [19,20]. Finally there were no significant differences in the interpretation of the results between our simulations for the Gompertz and logistic models.…”

“…Our results were compared with existing calculations of the logistic model [9,19] and [10]. In each of the Gompertz and logistic models we found that the both negative and positive correlation between additive and multiplicative noise were important in predicting the likely outcome of treatment protocols.…”

“…In Sec.IV we consider nonzero correlation time and present the results for the steady state properties of the Gompertz model driven by cross-correlated noise for the case of nonzero correlation time. We use our model to simulate the behaviour of the logistic model of [9], [19], and [10] and compare with the results obtained from the Gompertz model.…”

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

“…The logistic model has been used as a basic model of tumor cell growth. A more refined logistic model without immune response was presented in [24][25][26]. A similar model, including the presence of correlated noises for the case of correlation time, has also been considered [27].…”