In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the ...In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the controlling conditions for the extinction and persistence of the disease are obtained.Besides,the effects of the intensity of volatility Si and the speed of reversion 1 on the dynamical behaviors of the model are discussed.Finally,some numerical examples are given to support the theoretical results.The 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.展开更多
To counter the mass reproduction and penetration of crustacean zooplankton in Biological Activated Carbon(BAC)filters which may result in the presence of organisms in potable water and water pollution,this paper analy...To counter the mass reproduction and penetration of crustacean zooplankton in Biological Activated Carbon(BAC)filters which may result in the presence of organisms in potable water and water pollution,this paper analyzed the factors affecting organisms' reproduction in BAC filters.A comparative study was performed on the density and composition of crustacean zooplankton of the concerned water treatment units of two advanced water plants(Plant A and B)which with the same raw water and the same treatment technique in southern China.The results obtained show that the crustaceans' density and composition was very different between the sand filtered water of Plant A and Plant B.which Harpacticoida bred sharply in the sediment tanks and penetrated sand filter into BAC filters was the primary reason of crustaceans reproduce in BAC filters of Plant A.For prevention of the organisms reproduction in BAC,some strengthen measures was taken including pre-chlorination,cleaning coagulation tanks and sediment tanks completely,increasing sludge disposal frequency to stop organisms enter BAC filters,and the finished water quality was improved and enhanced.展开更多
全彩色3D打印技术是一种集智能化、定制化、多彩化于一体的增材制造工艺,其中粉基全彩色3D打印是研究时间最久、系统最完善、应用范围最广的技术。但不理想的表面颜色再现是阻碍其商业化的主要因素,并且缺乏完善的印刷图像颜色再现方法...全彩色3D打印技术是一种集智能化、定制化、多彩化于一体的增材制造工艺,其中粉基全彩色3D打印是研究时间最久、系统最完善、应用范围最广的技术。但不理想的表面颜色再现是阻碍其商业化的主要因素,并且缺乏完善的印刷图像颜色再现方法和颜色管理系统。因此,本研究整合了多种适合粉基3D打印的浸渍方法,使用3D Systems ProJet 860 Pro打印机打印24色卡和四基色立方体,比较不同组合浸渍处理后单平面和多平面的优化效果,选择最佳的浸渍方法,并提出了改进浸渍剂的方向。结果表明,浸渍过程可以大幅度增加3D打印模型表面颜色的饱和度,略微降低亮度,改善单平面以及多平面之间的色差。ColorBond和透明涂层喷剂的组合是最佳的浸渍方法,增加浸渍剂涂层均匀性、透明度、渗透性有利于进一步优化表面颜色。展开更多
Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those w...It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.展开更多
The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstl...The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstly prove the existence of local and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Secondly we show, by the construction of appropriate Lyapunov functions, that the uninfected equilibrium and the unique infected equilibrium of the mathematical model of HCV are globally asymptotically stable respectively when the threshold number and when .展开更多
基金supported by National Science and Technology Innovation 2030 of China Next-Generation Artificial Intelligence Major Project(Grant No.2018AAA0101800)Key Project of Technological Innovation and Application Development Plan of Chongqing(Grant No.cstc2020jscx-dxwtBX0044)+1 种基金Key projects of Mathematics and Finance Research Center of Sichuan University of Arts and Science(No.SCMF202201)National College Students Innovation and Entrepreneurship Training Program(No.S202110619028,202210619035).
文摘In this paper,a stochastic SiS epidemic infectious diseases model with double stochastic perturbations is proposed.First,the existence and uniqueness of the positive global solution of the model are proved.Second,the controlling conditions for the extinction and persistence of the disease are obtained.Besides,the effects of the intensity of volatility Si and the speed of reversion 1 on the dynamical behaviors of the model are discussed.Finally,some numerical examples are given to support the theoretical results.The 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.
基金Sponsored by the Major National S&T Program-Water Pollution and Governance(Grant No.2009ZX07423-003)
文摘To counter the mass reproduction and penetration of crustacean zooplankton in Biological Activated Carbon(BAC)filters which may result in the presence of organisms in potable water and water pollution,this paper analyzed the factors affecting organisms' reproduction in BAC filters.A comparative study was performed on the density and composition of crustacean zooplankton of the concerned water treatment units of two advanced water plants(Plant A and B)which with the same raw water and the same treatment technique in southern China.The results obtained show that the crustaceans' density and composition was very different between the sand filtered water of Plant A and Plant B.which Harpacticoida bred sharply in the sediment tanks and penetrated sand filter into BAC filters was the primary reason of crustaceans reproduce in BAC filters of Plant A.For prevention of the organisms reproduction in BAC,some strengthen measures was taken including pre-chlorination,cleaning coagulation tanks and sediment tanks completely,increasing sludge disposal frequency to stop organisms enter BAC filters,and the finished water quality was improved and enhanced.
文摘全彩色3D打印技术是一种集智能化、定制化、多彩化于一体的增材制造工艺,其中粉基全彩色3D打印是研究时间最久、系统最完善、应用范围最广的技术。但不理想的表面颜色再现是阻碍其商业化的主要因素,并且缺乏完善的印刷图像颜色再现方法和颜色管理系统。因此,本研究整合了多种适合粉基3D打印的浸渍方法,使用3D Systems ProJet 860 Pro打印机打印24色卡和四基色立方体,比较不同组合浸渍处理后单平面和多平面的优化效果,选择最佳的浸渍方法,并提出了改进浸渍剂的方向。结果表明,浸渍过程可以大幅度增加3D打印模型表面颜色的饱和度,略微降低亮度,改善单平面以及多平面之间的色差。ColorBond和透明涂层喷剂的组合是最佳的浸渍方法,增加浸渍剂涂层均匀性、透明度、渗透性有利于进一步优化表面颜色。
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
文摘It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.
文摘The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstly prove the existence of local and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Secondly we show, by the construction of appropriate Lyapunov functions, that the uninfected equilibrium and the unique infected equilibrium of the mathematical model of HCV are globally asymptotically stable respectively when the threshold number and when .
