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A stochastic SIS epidemic infectious diseases model with double stochastic perturbations

International Journal of Biomathematics 2024年第4期17卷 235-266页

作者： Xingzhi Chen Baodan Tian Xin Xu Ruoxi Yang Shouming Zhong School of Mathematics and Physics Southwest University of Science and TechnologyMianyangSichuan 621010P.R.China College of Mathematics and Statistics Chongqing University ChongqingChongqing 400000P.R.China School of Mathematical Sciences UESTC University of Electronic Science and Technology of China Chengdu Sichuan 611731P.R.China

In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is ***,the existence and uniqueness of the positive global solution of the model are ***,the controlling conditions for the extinction and persistence of the disease are ***,the effects of the intensity of volatility Si and the speed of reversion 1 on the dynamical behaviors of the model are ***,some numerical examples are given to support the theoretical *** results show that if the basic reproduction number R_(0)^(8)<1,the disease will be extinct,that is to say that we can control the threshold R_(0)^(8)to suppress the disease outbreak.

关键词： stochastic epidemic model Ornstein-Uhlenbeck process Brownian motion basic reproduction number extinction

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stochastic epidemic dynamics based on the association between susceptible and recovered individuals

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International Journal of Biomathematics 2021年第1期14卷 31-50页

作者： Luyao Xin Yingxin Guo Quanxin Zhu School of Mathematical Sciences Qufu Normal UniversityQufu 273165ShandongP.R.China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081HunanP.R.China

In this paper,we propose a new mathematical model based on the association between susceptible and recovered ***,we study the stability of this model with the deterministic case and obtain the conditions for the extinction of ***,in view of the association between susceptible and recovered individual perturbed by white noise,we also give sufficient conditions for the extinction and the permanence in mean of disease with the white ***,we have numerical simulations to demonstrate the correctness of obtained theoretical results.

关键词： Extinction permanence in mean stability stochastic epidemic model

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Exit problem of stochastic SIR model with limited medical resource

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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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Multi-patch multi-group epidemic model with varying infectivity

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Probability, Uncertainty and Quantitative Risk 2022年第4期7卷 333-364页

作者： Raphaël Forien Guodong Pang Étienne Pardoux INRAE Centre INRAE PACADomaine St-Paul-Site Agroparc84914 Avignon CedexFrance Department of Computational Applied Mathematics and Operations Research George R.Brown College of EngineeringRice UniversityHoustonTX 77005US Aix Marseille University CNRSI2M13453 MarseilleFrance

This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and distinct groups(possibly age groups).The limit is a set of Volterra-type integral equations,and the result shows the effects of both spatial and population *** novelty of the model is that the infectivity of an infected individual is infection age *** precisely,to each infected individual is attached a random infection-age dependent infectivity function,such that the various random functions attached to distinct individuals are *** proof involves a novel construction of a sequence of *** to invoke the law of large numbers for processes in,by using the solution of a MacKean-Vlasov type Poisson-driven stochastic equation(as in the propagation of chaos theory).We also establish an identity using the Feynman-Kac formula for an adjoint backward *** advantage of this approach is that it assumes much weaker conditions on the random infectivity functions than our earlier work for the homogeneous model in[20],where standard tightness criteria for convergence of stochastic processes were *** illustrate this new approach,we first explain the new proof under the weak assumptions for the homogeneous model,and then describe the multipatch-multigroup model and prove the law of large numbers for that model.

关键词： stochastic epidemic model Multi-patch multi-group Varying infectivity SIR model Law of large numbers Feynman-Kac formula Poisson-driven(McKean-Vlasov type)stochastic equations Propagation of chaos

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