Stationary distribution and extinction of a stochastic SEIS epidemic model motivated by Black–Karasinski process

Zhou, Baoquan; Shi, Ningzhong

doi:10.1016/j.aml.2023.108921

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…Wang et al studied a SIS model with the OU process and earn the reproduction number of the model to determine the stochastic extinction and persistence 3 . A stochastic SIRC model based on the OU process was analyzed by Zhiming et al 33 Zhou and Shi proposed the stationary distribution and extinction of a stochastic SEIS epidemic model motivated by Black Karasinski process 34 .…”

Section: Introductionmentioning

confidence: 99%

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Nabati

2024

Sci Rep

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The major objective of this paper is to examine a novel mean-reverting Ornstein–Uhlenbeck process-based stochastic SIRD model for transmission the epidemic disease that is a great crisis in numerous societies. For this purpose, the deterministic model is further converted into the stochastic form by allowing the infection rate satisfies the mean-reverting Ornstein–Uhlenbeck process to account the uncertainties involved in epidemic spread. At first using Lyapunov functions, the solution’s uniqueness and positivity will be demonstrated. Subsequently, the stochastic epidemic threshold $$\Re_{0}^{S}$$ ℜ 0 S that controls the disease’s extinction and persistence in the mean is identified analytically. It has been established that when $$\Re_{0}^{S} < 1$$ ℜ 0 S < 1 the disease will extinguish, whereas if $$\Re_{0}^{S} > 1$$ ℜ 0 S > 1 the disease is persistent. At last, several numerical simulations are presented to demonstrate the findings of the hypothetical investigation results. These simulations served to vividly illustrate and validate the implications derived from the hypothetical analysis.

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Section: Introductionmentioning

confidence: 99%

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Nabati

2024

Sci Rep

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Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

Zhou,

Shi

2024

Chaos, Solitons & Fractals

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Stationary distribution and extinction of a stochastic SEIS epidemic model motivated by Black–Karasinski process

Cited by 2 publications

References 10 publications

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Introducing a novel mean-reverting Ornstein–Uhlenbeck process based stochastic epidemic model

Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

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