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exit problem of stochastic SIR model with limited medical resource

Theoretical & Applied Mechanics Letters 2023年第1期13卷 8-13页

作者： Y.C.Mao X.B.Liu State Key Lab of Mechanics and Control for Mechanical Structures College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China

Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the ***,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter *** this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with ***,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.

关键词： Stochastic epidemic model Stochastic dynamical system Large deviation theory exit problem

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Diffusion occupation time before exiting

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Frontiers of Mathematics in China 2014年第4期9卷 843-861页

作者： Yingqiu LI Suxin WANG Xiaowen ZHOU Na ZHU College of Mathematics and Computing Sciences Changsha University of Science and Technology Changsha 410004 China College of Mathematics Nankai University Tianjin 300071 China Department of Mathematics and Statistics Concordia University MontrealQuebec H3G 1M8 Canada

Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.

关键词： Diffusion exit problem occupation time occupation density localtime Brownian motion with two-valued drift skew Ornstein-Uhlenbeck (OU)process

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exit identities for diusion processes observed at Poisson arrival times

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Frontiers of Mathematics in China 2020年第3期15卷 507-528页

作者： Yingqiu LI Ye CHEN Shilin WANG Zhaohui PENG School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410004China College of Mathematics and Physics Hunan University of Arts and ScienceChangde 415000China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha 410004China

For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson *** results are expressed in terms of solutions to the ... 详细信息

关键词： Time-homogeneous diffusion process exit problem Poisson arrival time Brownian motion

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