Stochastic behaviors of an improved Gompertz tumor growth model with coupled two types noise

Huijun Lv; Guitian He; Hui Cheng; Yun Peng

doi:10.1016/j.heliyon.2022.e11574

Stochastic behaviors of an improved Gompertz tumor growth model with coupled two types noise

Heliyon. 2022 Nov 11;8(11):e11574. doi: 10.1016/j.heliyon.2022.e11574. eCollection 2022 Nov.

Authors

Huijun Lv¹, Guitian He¹, Hui Cheng¹, Yun Peng¹

Affiliation

¹ College of Mathematics and Physics, Center for Applied Mathematics of Guangxi Minzu University, Nanning 530006, China.

Abstract

In this work, an improved Gompertz tumor growth model has been introduced. The expressions of steady probability distributions (SPD) of stochastic Gompertz tumor growth models are studied by using the technique of Fokker-Planck equation (FPE), and their dynamic behaviors are also further investigated. Moreover, the expressions for mean, variance, skewness, as well as the mean first-passage time (MFPT) also have been derived. And the influence of noise intensity, correlation coefficient, and noise correlation time of SPD are further analyzed. It is worthy noting that the colored noise intensity has an important impact on SPD. Furthermore, adjusting birth and death parameters also significantly impact SPD, MFPT, mean, variance as well as skewness.

Keywords: Colored noise; Fokker-Planck equation; Improved Gompertz tumor growth model; Skewness.