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

Ying Zhang1, Wei Li1,*, Guidong Yang1, Snezana Kirin2

1 School of Mathematics and Statistics, Xidian University, Xi’an, 710071, China
2 Innovation Center of Faculty of Mechanical Engineering, Belgrade, 11100, Serbia

* Corresponding Author: Wei Li. Email: email

Computer Modeling in Engineering & Sciences 2024, 138(3), 2177-2199. https://doi.org/10.32604/cmes.2023.030728

Abstract

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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APA Style
Zhang, Y., Li, W., Yang, G., Kirin, S. (2024). Analytical and numerical methods to study the MFPT and SR of a stochastic tumor-immune model. Computer Modeling in Engineering & Sciences, 138(3), 2177-2199. https://doi.org/10.32604/cmes.2023.030728
Vancouver Style
Zhang Y, Li W, Yang G, Kirin S. Analytical and numerical methods to study the MFPT and SR of a stochastic tumor-immune model. Comput Model Eng Sci. 2024;138(3):2177-2199 https://doi.org/10.32604/cmes.2023.030728
IEEE Style
Y. Zhang, W. Li, G. Yang, and S. Kirin "Analytical and Numerical Methods to Study the MFPT and SR of a Stochastic Tumor-Immune Model," Comput. Model. Eng. Sci., vol. 138, no. 3, pp. 2177-2199. 2024. https://doi.org/10.32604/cmes.2023.030728



cc Copyright © 2024 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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