A stochastic turbidostat model with Ornstein-Uhlenbeck process: dynamics analysis and numerical simulations

Article Mathematics, Interdisciplinary Applications

Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies

Baoquan Zhou et al.

Summary: This study discusses a stochastic epidemic model that takes into account the impact of vaccination and the unpredictability of natural environmental variations. By constructing Lyapunov functions, the existence condition for the model's ergodic stationary distribution is determined, and a quasi-endemic equilibrium related to the deterministic system's endemic equilibrium is defined. An exact expression of the probability density function around the quasi-endemic equilibrium is derived, which reflects the dynamic properties of the epidemic system.

CHAOS SOLITONS & FRACTALS (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, Interdisciplinary Applications

Stochastic dynamics of populations with refuge in polluted turbidostat

Yu Mu et al.

Summary: This work investigates a turbidostat model with toxicant and prey refuge under deterministic and stochastic environments. The study analyzes the existence and uniqueness of positive solutions under the effect of shelter and stochastic perturbation, as well as determines the conditions of extinction and permanence for each population with the impact of toxicant and prey refuge under stochastic environment. The results reveal the dynamics of populations under the influence of these factors, with numerical examples provided to verify the theoretical analysis and simulate the effects on population dynamics in both deterministic and stochastic cases.

CHAOS SOLITONS & FRACTALS (2021)

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Article Mathematics, Interdisciplinary Applications