Stochastic dynamic analysis of a chemostat model of intestinal microbes with migratory effect

Yue Dong; Xinzhu Meng; Yue Dong; Xinzhu Meng

doi:10.3934/math.2023321

AIMS Mathematics

2023, Volume 8, Issue 3: 6356-6374. doi: 10.3934/math.2023321

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Research article

Stochastic dynamic analysis of a chemostat model of intestinal microbes with migratory effect

Yue Dong ,
Xinzhu Meng ^,

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 28 October 2022 Revised: 16 December 2022 Accepted: 20 December 2022 Published: 03 January 2023
MSC : 37A50, 37H05, 37N25, 60G10

This paper proposes a stochastic intestinal chemostat model considering microbial migration, intraspecific competition and stochastic perturbation. First, the extinction and persistence in mean of the intestinal microbe of the chemostat model are investigated by constructing the appropriate Lyapunov functions. Second, we explore and obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the model by using ergodic theory. The results show stochastic interference has a critical impact on the extinction and sustainable survival of the intestinal microbe. Eventually, numerical simulations are carried out to verify the theoretical results.
- stochastic chemostat model,
- microbial migration,
- extinction,
- persistence in mean,
- stationary distribution
Citation: Yue Dong, Xinzhu Meng. Stochastic dynamic analysis of a chemostat model of intestinal microbes with migratory effect[J]. AIMS Mathematics, 2023, 8(3): 6356-6374. doi: 10.3934/math.2023321

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Abstract

This paper proposes a stochastic intestinal chemostat model considering microbial migration, intraspecific competition and stochastic perturbation. First, the extinction and persistence in mean of the intestinal microbe of the chemostat model are investigated by constructing the appropriate Lyapunov functions. Second, we explore and obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the model by using ergodic theory. The results show stochastic interference has a critical impact on the extinction and sustainable survival of the intestinal microbe. Eventually, numerical simulations are carried out to verify the theoretical results.

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