Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises
Abstract
In this paper, a two-stage tumor-immune system with Gaussian white noises is investigated in order to understand the interaction mechanism between tumor cells and the immune system. Based on Langevin theory and the Fokker–Planck (FP) equation, a set of differential equations that governing the second-order moments of cells are obtained and solved. Following this, the statistical properties including the volatility of cell density, Fano factor, sensitivity analysis are discussed, respectively. It is concluded that mature immune cells around the tumor-free state change in a bigger range with regard to the noise intensity. However, the tumor cells around the tumor-present state have remarkable volatility all the time no matter what size of the noise intensity. In addition, the relative size of fluctuation described by Fano factors illustrates that Michaelis saturation coefficient and killing rate can bring larger fluctuation to the tumor cells, but dead rate and proliferation rate can gre...atly affect the fluctuation size of the mature immune cells. The sensitivity coefficients of three kinds of cells proved that the density of tumor cells are sensitively influenced by all the parametric values, but the mature immune cells are almost independent of the differentiation rate during the process from the immature to the mature immune cells.
Keywords:
Tumor-immune system / Stability analysis / Gaussian white noise / Fokker–Planck equationSource:
International Journal of Dynamics and Control, 2022Publisher:
- Springer Science and Business Media Deutschland GmbH
Funding / projects:
- Natural Science Basic Research Program of Shaanxi (Nos. 2021 JM-116, 2021 JM-118), “One belt, one road” Introduction of High-honor Foreign Experts Project (No. DL20200027009)
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Institution/Community
Mašinski fakultetTY - JOUR AU - Li, Wei AU - Li, M. AU - Trišović, Nataša PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3830 AB - In this paper, a two-stage tumor-immune system with Gaussian white noises is investigated in order to understand the interaction mechanism between tumor cells and the immune system. Based on Langevin theory and the Fokker–Planck (FP) equation, a set of differential equations that governing the second-order moments of cells are obtained and solved. Following this, the statistical properties including the volatility of cell density, Fano factor, sensitivity analysis are discussed, respectively. It is concluded that mature immune cells around the tumor-free state change in a bigger range with regard to the noise intensity. However, the tumor cells around the tumor-present state have remarkable volatility all the time no matter what size of the noise intensity. In addition, the relative size of fluctuation described by Fano factors illustrates that Michaelis saturation coefficient and killing rate can bring larger fluctuation to the tumor cells, but dead rate and proliferation rate can greatly affect the fluctuation size of the mature immune cells. The sensitivity coefficients of three kinds of cells proved that the density of tumor cells are sensitively influenced by all the parametric values, but the mature immune cells are almost independent of the differentiation rate during the process from the immature to the mature immune cells. PB - Springer Science and Business Media Deutschland GmbH T2 - International Journal of Dynamics and Control T1 - Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises DO - 10.1007/s40435-022-00959-9 ER -
@article{ author = "Li, Wei and Li, M. and Trišović, Nataša", year = "2022", abstract = "In this paper, a two-stage tumor-immune system with Gaussian white noises is investigated in order to understand the interaction mechanism between tumor cells and the immune system. Based on Langevin theory and the Fokker–Planck (FP) equation, a set of differential equations that governing the second-order moments of cells are obtained and solved. Following this, the statistical properties including the volatility of cell density, Fano factor, sensitivity analysis are discussed, respectively. It is concluded that mature immune cells around the tumor-free state change in a bigger range with regard to the noise intensity. However, the tumor cells around the tumor-present state have remarkable volatility all the time no matter what size of the noise intensity. In addition, the relative size of fluctuation described by Fano factors illustrates that Michaelis saturation coefficient and killing rate can bring larger fluctuation to the tumor cells, but dead rate and proliferation rate can greatly affect the fluctuation size of the mature immune cells. The sensitivity coefficients of three kinds of cells proved that the density of tumor cells are sensitively influenced by all the parametric values, but the mature immune cells are almost independent of the differentiation rate during the process from the immature to the mature immune cells.", publisher = "Springer Science and Business Media Deutschland GmbH", journal = "International Journal of Dynamics and Control", title = "Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises", doi = "10.1007/s40435-022-00959-9" }
Li, W., Li, M.,& Trišović, N.. (2022). Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises. in International Journal of Dynamics and Control Springer Science and Business Media Deutschland GmbH.. https://doi.org/10.1007/s40435-022-00959-9
Li W, Li M, Trišović N. Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises. in International Journal of Dynamics and Control. 2022;. doi:10.1007/s40435-022-00959-9 .
Li, Wei, Li, M., Trišović, Nataša, "Dynamical analysis of a kind of two-stage tumor-immune model under Gaussian white noises" in International Journal of Dynamics and Control (2022), https://doi.org/10.1007/s40435-022-00959-9 . .