Journal ArticleDOI
Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein-Uhlenbeck process
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TLDR
Wang et al. as mentioned in this paper proposed a stochastic epidemic model with media coverage and two mean-reverting Ornstein-Uhlenbeck processes, and they theoretically proved that the solution to the model is unique and global, as well as the existence of an ergodic stationary distribution.About:
This article is published in Mathematics and Computers in Simulation.The article was published on 2022-01-01. It has received 20 citations till now. The article focuses on the topics: Computer science & Ornstein–Uhlenbeck process.read more
Citations
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Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process
Zhen–Feng Shi,Daqing Jiang +1 more
TL;DR: In this article , the authors developed a HTLV-I infection model with general infection form, and obtained sufficient conditions for the existence and uniqueness of the ergodic stationary distribution for the stochastic model.
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Stationary distribution and extinction of a stochastic SVEIS epidemic model incorporating Ornstein-Uhlenbeck process
Yunquan Song,Xinong Zhang +1 more
TL;DR: In this paper , a new stochastic SVEIS epidemic model was proposed, which satisfies the mean-reverting Ornstein-Uhlenbeck process, and proved that this model has a stationary distribution when the critical value R 0s>1.
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Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process
Qun Liu,Daqing Jiang +1 more
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Global dynamics and density function in a class of stochastic SVI epidemic models with Lévy jumps and nonlinear incidence
TL;DR: In this paper , the global dynamics and probability density function for a class of stochastic SVI epidemic models with white noise, Lévy jumps and nonlinear incidence were studied.
References
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A contribution to the mathematical theory of epidemics
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
A Contribution to the Mathematical Theory of Epidemics.
TL;DR: The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
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An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
TL;DR: The article is built around $10$ MATLAB programs, and the topics covered include stochastic integration, the Euler--Maruyama method, Milstein's method, strong and weak convergence, linear stability, andThe stochastics chain rule.
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Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
TL;DR: The Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences as mentioned in this paper is a popular reference book for physics, chemistry and the natural sciences that is used in many applications.
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Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: In this paper, the authors developed criteria for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator, and applied the criteria to several specific processes, including linear stochastic systems under nonlinear feedback, work-modulated queues, general release storage processes and risk processes.