Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise

Hao, Mu; Jia, Wantao; Wang, Liang; Li, Fu-Xiao

doi:10.1016/j.chaos.2022.112765

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…Many studies have shown that noise and time delay affect the transition between different steady states of tumor populations [19][20][21][22][23][24][25][26][27][28][29][40][41][42][43][44][45][46][47][48][49]. What sets this paper apart from previous research is that Gaussian white noise, Lévy noise and time delay are considered synergistically, and the results provide certain guidance for better study of the growth law of tumors, improve the treatment method of tumors, and enhance the level of tumor treatment.…”

Section: Discussionmentioning

confidence: 97%

“…In fact, Lévy noise, as a typical non-Gaussian noise, plays an irreplaceable role in the system and cannot be ignored, with properties such as long trailing and discontinuous jumps, which can jump over a wide range and can more accurately reflect the disturbances in reality [30][31][32][33][34][35][36][37][38][39]. However, the process of tumor growth can also be affected by sudden or extreme events, so Lévy noise is more realistic and has a wider application [40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

Yu,

Guo,

Chen

2024

Phys. Scr.

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In this paper, we analyze the dynamical behavior of a delayed tumor growth model under the joint effect of Gaussian white noise and Lévy noise by studying the mean first passage time (MFPT) and stochastic resonance (SR). Firstly, the tumor growth model under the joint effect of Gaussian white noise, Lévy noise and time delay is introduced. Then, the Lévy noise sequence is simulated by Janicki-Weron algorithm, and the MFPT and signal-to-noise ratio(SNR) of the system are simulated by using fourth-order stochastic Runge-Kutta algorithm. The effects of noise parameters, time delay and periodic signal parameters on MFPT, SR are discussed in detail, respectively. In addition, we find the phenomenon of noise enhanced stability. The results of the study can help to select the optimal regulatory parameters in the tumor growth model and promote the treatment of tumors.

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Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

Yu,

Guo,

Chen

2024

Phys. Scr.

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“…In recent years, a varieties of tumor diseases have been observed and brought a revolution in the field of cancer treatment. In order to explore the law of tumor growth and extinction, a good many of researchers dedicate to study the tumor models, the issues including the growth of anti-tumor, the competition between the tumor cells and the immune system [1][2][3][4][5]. Some deterministic tumor models such as Logistic model [6], Gompertz model [7] have been proved to be the powerful models to describe the dynamical evolution of the tumor, these models are not only helpful for understanding the competition between the tumor cells and the immune system, but also beneficial for assisting the tumor's elimination or extinction.…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Methods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

Zhang,

Li,

Yang

et al. 2024

CMES

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The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model with noise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian white noise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. As follows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPT is obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrence of the tumor from the extinction state to the tumor-present state is more concerned in this paper. A more efficient algorithm of Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of the theoretical SPD and MFPT. With the existence of a weak signal, the functional relationship between Signal-to-Noise Ratio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicative Gaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and the multiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasing intensity of the additive Gaussian white noise results in the minimum of MFPT. In addition, the correlation times are negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise and the Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonously increased in the case of Gaussian white noise with the change of the correlation time. At last, the optimal parameters in BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural network layers and the number of nodes in each layer.

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Tumor state transitions driven by Gaussian and non-Gaussian noises

Hua

2023

Mechanobiology in Medicine

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Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise

Cited by 3 publications

References 33 publications

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

Analytical and Numerical Methods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

Tumor state transitions driven by Gaussian and non-Gaussian noises

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