DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION

Weili Liu; Hongpeng Zhang; Weipeng Zhang; Xuenan Sun

doi:10.11948/20220558

2023 Volume 13 Issue 5

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Weili Liu, Hongpeng Zhang, Weipeng Zhang, Xuenan Sun. DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2739-2766. doi: 10.11948/20220558

Citation:

Weili Liu, Hongpeng Zhang, Weipeng Zhang, Xuenan Sun. DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2739-2766. doi: 10.11948/20220558

DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION

1.
School of Mathematics and Statistics, Northeast Normal University, No. 5268 Renmin Street, 130024, Changchun, Jilin, China

Author Bio: Email: liuwl1661@nenu.edu.cn(W. Liu); Email: zhanghp767@nenu.edu.cn(H. Zhang); Email: sunxn107@nenu.edu.cn(X. Sun)
Corresponding author: Email: zhangwp996@nenu.edu.cn(W. Zhang)

Abstract

Abstract

This paper mainly explores the stochastic behaviors of the interaction between tumor cells and immune cells when vitamins are added. First, it is shown that the stochastic tumor-immune-vitamin model has a unique global positive solution. Second, we obtain that the solution of our model is stochastically ultimately bounded, stochastically permanent, extinct and persistent in mean under some threshold conditions. Moreover, when the perturbation is weak, the stochastic model has a unique stationary distribution. Finally, numerical simulations are performed to verify the theoretical results.
- Tumor-immune-vitamin model /
- stochastic process /
- extinction /
- persistence /
- stationary distribution
MSC: 60H10, 65C20

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References

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