Dynamics of stochastic chemostat models with mixed nonlinear incidence

Article Mathematics, Applied

Stationary distribution of a chemostat model with distributed delay and stochastic perturbations

Miaomiao Gao et al.

Summary: This paper considers a Lotka-Volterra food chain chemostat model with distributed delay and stochastic perturbations, obtaining conditions for the existence of a stationary distribution where two species can coexist in the long term.

APPLIED MATHEMATICS LETTERS (2022)

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Article Biology

Competitive Exclusion in a General Multi-species Chemostat Model with Stochastic Perturbations

Chaoqun Xu et al.

Summary: This study introduces a stochastic competition chemostat model, and proves the applicability of the competitive exclusion principle in this model. Experimental evidence shows that environmental noise may lead to the exchange of destinies between two microorganism species in the chemostat.

BULLETIN OF MATHEMATICAL BIOLOGY (2021)

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Article Biology

Global dynamics of the chemostat with overflow metabolism

Carlos Martinez et al.

Summary: The paper investigates overflow metabolism in a chemostat model, proving the existence of at most one steady-state with microorganism presence, and discussing its application in biomass production or recombinant protein production.

JOURNAL OF MATHEMATICAL BIOLOGY (2021)

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Article Mathematics, Applied

A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function

Xiaofeng Zhang et al.

Summary: In this paper, a stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function is constructed and analyzed, showing the existence of global unique positive solution, extinction exponentially, and persistence in the mean of microorganism. Numerical simulations support the conclusions that the mean-reverting process effectively introduces environmental noise and the reversion speed and volatility intensity impact the extinction and persistence of microorganism significantly.

APPLIED MATHEMATICS AND COMPUTATION (2021)

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Article Mathematics, Applied

Determining the competition outcome in the chemostat: General response functions and delayed growth

Xinxin Wang et al.

Summary: By constructing a novel Liapunov functional, this study shows that only one species can survive when competing for a single essential resource in a chemostat. The result is applicable to chemostat competition models with differential removal rates, delayed growth, and general response functions.

APPLIED MATHEMATICS LETTERS (2021)

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Article Mathematics, Interdisciplinary Applications

Noise-induced stochastic transition: A stochastic chemostat model with two complementary nutrients and flocculation effect

Rong Liu et al.

Summary: This study investigates a novel stochastic chemostat model with two complementary nutrients and the flocculation effect. By constructing appropriate stochastic Lyapunov functions, the existence of an ergodic stationary distribution and persistence of the stochastic model are discussed. Numerical simulations show that random fluctuation can lead to a transition from extinction to persistence in microbial growth in the chemostat.

CHAOS SOLITONS & FRACTALS (2021)

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Article Mathematics, Applied

Dynamics of stochastic HTLV-I infection model with nonlinear CTL immune response

Daipeng Kuang et al.

Summary: In this paper, the dynamics of a stochastic human T-cell leukemia virus type I (HTLV-I) infection model with cytotoxic T lymphocyte (CTL) immune response is investigated. The study shows the unique positive global solution, stochastic permanence and ultimate boundedness of the model. Sufficient conditions for the ergodic stationary distribution and the virus extinction threshold R0* are also established, with numerical simulations illustrating the theoretical results.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

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Article Computer Science, Interdisciplinary Applications

Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics

Haokun Qi et al.

Summary: This paper investigates the dynamics of an HIV system considering stochastic environmental fluctuations, with discussions on the global positive solution, stochastically ultimate boundedness, and long-time asymptotic properties of the system. The study shows that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV, as demonstrated in numerous numerical simulations.

MATHEMATICS AND COMPUTERS IN SIMULATION (2021)

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Article Mathematics, Applied