Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance

Yan Fu; Tian Lu; Meng Zhou; Dongwei Liu; Qihang Gan; Guowei Wang; Yan Fu; Tian Lu; Meng Zhou; Dongwei Liu; Qihang Gan; Guowei Wang

doi:10.3934/mbe.2023957

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 21626-21642. doi: 10.3934/mbe.2023957

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Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance

1.
School of Mathematics & Computer Science, Yuzhang Normal University, Nanchang 330103, China
2.
School of Education, Nanchang Institute of Science & Technology, Nanchang 330108, China

Academic Editor: Mingji Zhang

Received: 15 October 2023 Revised: 27 November 2023 Accepted: 30 November 2023 Published: 06 December 2023

Based on the Michaelis-Menten reaction model with catalytic effects, a more comprehensive one-dimensional stochastic Langevin equation with immune surveillance for a tumor cell growth system is obtained by considering the fluctuations in growth rate and mortality rate. To explore the impact of environmental fluctuations on the growth of tumor cells, the analytical solution of the steady-state probability distribution function of the system is derived using the Liouville equation and Novikov theory, and the influence of noise intensity and correlation intensity on the steady-state probability distributional function are discussed. The results show that the three extreme values of the steady-state probability distribution function exhibit a structure of two peaks and one valley. Variations of the noise intensity, cross-correlation intensity and correlation time can modulate the probability distribution of the number of tumor cells, which provides theoretical guidance for determining treatment plans in clinical treatment. Furthermore, the increase of noise intensity will inhibit the growth of tumor cells when the number of tumor cells is relatively small, while the increase in noise intensity will further promote the growth of tumor cells when the number of tumor cells is relatively large. The color cross-correlated strength and cross-correlated time between noise also have a certain impact on tumor cell proliferation. The results help people understand the growth kinetics of tumor cells, which can a provide theoretical basis for clinical research on tumor cell growth.
- tumor cells,
- Langevin equation,
- noise,
- relevance,
- immune mechanism,
- Fokker-Planck equation
Citation: Yan Fu, Tian Lu, Meng Zhou, Dongwei Liu, Qihang Gan, Guowei Wang. Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 21626-21642. doi: 10.3934/mbe.2023957

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Abstract

Based on the Michaelis-Menten reaction model with catalytic effects, a more comprehensive one-dimensional stochastic Langevin equation with immune surveillance for a tumor cell growth system is obtained by considering the fluctuations in growth rate and mortality rate. To explore the impact of environmental fluctuations on the growth of tumor cells, the analytical solution of the steady-state probability distribution function of the system is derived using the Liouville equation and Novikov theory, and the influence of noise intensity and correlation intensity on the steady-state probability distributional function are discussed. The results show that the three extreme values of the steady-state probability distribution function exhibit a structure of two peaks and one valley. Variations of the noise intensity, cross-correlation intensity and correlation time can modulate the probability distribution of the number of tumor cells, which provides theoretical guidance for determining treatment plans in clinical treatment. Furthermore, the increase of noise intensity will inhibit the growth of tumor cells when the number of tumor cells is relatively small, while the increase in noise intensity will further promote the growth of tumor cells when the number of tumor cells is relatively large. The color cross-correlated strength and cross-correlated time between noise also have a certain impact on tumor cell proliferation. The results help people understand the growth kinetics of tumor cells, which can a provide theoretical basis for clinical research on tumor cell growth.

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