Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

Exit problem of stochastic SIR model with limited medical resource

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 evolution.However,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 value.In 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 epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.

Application of Statistical Tools for Data Analysis and Interpretation in Rice Plant Pathology

There has been a significant advancement in the application of statistical tools in plant pathology during the past four decades. These tools include multivariate analysis of disease dynamics involving principal component analysis, cluster analysis, factor analysis, pattern analysis, discriminant analysis, multivariate analysis of variance, correspondence analysis, canonical correlation analysis, redundancy analysis, genetic diversity analysis, and stability analysis, which involve in joint regression, additive main effects and multiplicative interactions, and genotype-by-environment interaction biplot analysis. The advanced statistical tools, such as non-parametric analysis of disease association, meta-analysis, Bayesian analysis, and decision theory, take an important place in analysis of disease dynamics. Disease forecasting methods by simulation models for plant diseases have a great potentiality in practical disease control strategies. Common mathematical tools such as monomolecular, exponential, logistic, Gompertz and linked differential equations take an important place in growth curve analysis of disease epidemics. The highly informative means of displaying a range of numerical data through construction of box and whisker plots has been suggested. The probable applications of recent advanced tools of linear and non-linear mixed models like the linear mixed model, generalized linear model, and generalized linear mixed models have been presented. The most recent technologies such as micro-array analysis, though cost effective, provide estimates of gene expressions for thousands of genes simultaneously and need attention by the molecular biologists. Some of these advanced tools can be well applied in different branches of rice research, including crop improvement, crop production, crop protection, social sciences as well as agricultural engineering. The rice research scientists should take advantage of these new opportunities adequately in adoption of the new highly potential advanced technologies while planning experimental designs, data collection, analysis and interpretation of their research data sets.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number Ro, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if Ro is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If Ro is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of Ro, when the stochastic system obeys some conditions and Ro is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.

The Game-Theoretical Model of Using Insecticide-Treated Bed-Nets to Fight Malaria

Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.

Fast Solvers of Fredholm Optimal Control Problems

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

Epidemic Diseases and Chinese Medicine: Example of SARS and COVID-19: Part Two

Along with the legends about epidemic demons,China has developed over the centuries a medical approach to epidemic diseases based on the teachings of Hucng Di Nei Jing(《黄帝内经》Huangdi s Intermnal Classic),Nan Jing(《难经》Classic of Difficult Issues),and Shang Han Lun(《伤寒论》Treatise on Cold Damage).Other doctors and scientists participated in this evolution of knowledge,like Wang Shuhe(王叔和),Ge Hong(葛洪),Chao Yuanfang(巢元方),Sun Simiao(孙思邈),and Liu Wansu(刘完素).However,it was in the 17^th century,after the great break of the Song,Jin,and Yuan eras that an innovative spirit,Wu Youke(吴又可1582-1652)first foresaw the existence of microorganisms as we know them now.His Wen Yi Lun(《瘟疫论》Treatise on Pestilence)foreshadows an original approach to epidemic diseases,particularly emerging infectious diseases of the 21^st century.After them,traditional Chinese medicine developed a comprehensive method of diagnosing and treating of these diseases(Epidemic Diseases Theory瘟疫学说)within the School ofHeat Diseases(温病学派).In a third article,we will examine some applications in the treatment of the SARS 2003-2004 epidemic(非典型肺炎)and the current COVID-19(新型冠状病毒肺炎)pandemic.

The Impact of the News Frames on Report of the 2020 Pandemic in China’s National Media

News frames is a general application of the Frame Theory in journalistic practice,and the setting of the Frame Theory in news media,to some extent,may make the news agency have more choices of the topics,more channels of the report,and more impacts on readers and audiences.It is for this reason that news media are very interested in setting up their news frame to guide their reportage.It won’t be surprised that when important affairs took place,the media set a theme for their coverage;while at the same time,audiences recognized that they are allowed to know the facts as well to evaluate the events properly.The coverage of disaster news is one of the concrete examples.However,when reading the reportage framework of the news in China,it can be seen that media would be likely to set similar frames for the focus of the report,and this potentially created complexity and difficulty in analyzing disaster news events in terms of content classification,reporting form,and news-making on effectiveness.The outbreak of the 2020 COVID-19 gathered media to work on a centralized proposal–anti-epidemic,so that textual,audio-visual contents and other forms of reporting show a diversified perspective for disaster news.This reporting form is a new challenge for Chinese news media,reflected in their practice on how Chinese government and people fought against the virus,how Chinese medical community dispatched their team to assist COVID-19 fight,and how Chinese media responded to the vilification of foreign media during that period.This paper takes three established media Hubei Daily,CCTV and China Daily as examples for an in-depth analysis.

Epidemic Diseases and Chinese Medicine:Example of SARS and COVID‑19:Part Two

Along with the legends about epidemic demons,China has developed over the centuries a medical approach to epidemic diseases based on the teachings of Huang Di Nei Jing(《黄帝内经》Huangdi’s Internal Classic),Nan Jing(《难经》Classic of Difficult Issues),and Shang Han Lun(《伤寒论》Treatise on Cold Damage).Other doctors and scientists participated in this evolution of knowledge,like Wang Shuhe(王叔和),Ge Hong(葛洪),Chao Yuanfang(巢元方),Sun Simiao(孙思邈),and Liu Wansu(刘完素).However,it was in the 17th century,after the great break of the Song,Jin,and Yuan eras that an innovative spirit,Wu Youke(吴又可1582–1652)first foresaw the existence of microorganisms as we know them now.His Wen Yi Lun(《瘟疫论》Treatise on Pestilence)foreshadows an original approach to epidemic diseases,particularly emerging infectious diseases of the 21st century.After them,traditional Chinese medicine developed a comprehensive method of diagnosing and treating of these diseases(Epidemic Diseases Theory瘟疫学说)within the School of Heat Diseases(温病学派).In a third article,we will examine some applications in the treatment of the SARS 2003–2004 epidemic(非典型肺炎)and the current COVID-19(新型冠状病毒肺炎)pandemic.

基于疫苗接种的SEIHRVI传染病模型分析与最优控制

为研究疫苗接种对控制传染病的影响,建立了具有标准发生率的传染病模型。通过推导得出模型的基本再生数,给出地方病平衡点的存在条件。借助构造Lyapunov函数证明了平衡点的全局稳定性。应用Pontryagin最大值原理分析了最优控制问题,得出最优控制策略。结果表明:提高疫苗接种率和效力能有效控制疾病传播;注意自我保护,及时接种以及重视治疗一定程度上可减小疾病爆发的规模。

清代瘟疫学家辨治疫病理论与经验探析

清代瘟疫学家结合治疫经验,对疫病病因、传变和辨治理论进行了补充与发展。在病因方面,遵杂气致疫,对杂气属性有更全面的认识。在传变与辨治方面,戴天章提倡表里传变与辨治;一些医家创以中道为中心的传变与辨治理论,如余师愚的毒热入胃布散十二经的理论、李炳的浊邪壅闭肺胃理论、朱增籍的沴邪直干肺胃理论;一些医家重视三焦传变与辨治,如杨栗山的三焦怫热郁滞理论、朱增籍的沴邪郁结三焦理论;此外,刘奎、朱增籍遵六经传变与辨治。清代瘟疫学家辨治疫病理论与经验对当代防治疫病有指导与启发意义。在当今时代,诸家所展现的变通和创新思维在防治新发和突发传染病方面显得尤为重要。

承诺理论视角下辟谣短视频分享意愿的驱动因素

短视频平台已成为公众获取与利用健康信息的重要渠道。新冠等病毒近年不断流行,涉疫谣言通过短视频平台传播并被用户采纳,为此,分析辟谣短视频分享意愿的驱动因素,有助于公众参与谣言治理,深化网络生态治理。文章采用问卷调查法,收集321份不同年龄层的有效样本,基于承诺理论对情感承诺、持续承诺、规范承诺等构念进行短视频平台下的情境化,以探究情感承诺、持续承诺、规范承诺的前置要素及其对辟谣短视频分享意愿的影响。研究发现:社交圈群认同、平台卷入度显著正向影响情感承诺;时间成本、社交网络形象显著正向影响持续承诺;集体主义、利他主义显著正向影响规范承诺;情感承诺、规范承诺显著正向影响辟谣短视频分享意愿,而持续承诺的影响不显著。

齐鲁医家刘奎《松峰说疫》对《黄帝内经》防疫思想的传承创新

《松峰说疫》由齐鲁医家刘奎所著,其承袭并创新了《黄帝内经》中的疫病预防与治疗理论。基于天人相应与伏邪致病等理论,倚重运气四时,强调元气的重要性,并重视邪虚、毒气等致病因素,阐释了伏邪致病机制,并提出瘥后防复的策略。《松峰说疫》还专设“避瘟方”,通过内外兼治、鲜药护正、芳香解毒以及妙用单药等多种创新性方法,丰富了疫病预防的理论与实践。此外,刘奎还强调了防治结合的治疗理念,通过内服解毒、汗吐法及外治针刮、罨熨法等多种治疗手段,为疫病的治疗提供了丰富的选择方案。《松峰说疫》不仅促进了《黄帝内经》理论的传承与创新,还丰富了疫病预防的途径和方法,为临床防治传染病提供了宝贵的新思路,具有深远的学术价值和实际意义。

吴鞠通从运气学说论治疫病思想探析

清代医家吴鞠通重视运用运气学说论治疫病。吴鞠通认为疫病病邪主要是厉气夹杂秽浊,疫病有温疫、寒疫之分,无论温疫、寒疫的发生均与运气条件有着密切的联系,处方用药更需根据疫病发生的运气学特点配伍化裁。吴鞠通以每年的五运六气条件结合更大时间范围的三元甲子类四时论,对于疫病理论进行了阐发,为丰富当代疫病诊疗理论提供了重要的借鉴。

Detection Method for Cascading Failure of Power Systems Based on Epidemic Model

The early detection of cascading failure plays an important role in the safe and stable operation of the power system with high penetration of renewable energy.This paper proposes a fault propagation dynamic model based on the epidemic model,and further puts forward a method to detect the development of cascading failures.Through the simulation of the IEEE 39-bus and 118-bus systems,this model is proven to be valid and capable of providing practical technical support for the prevention of cascading failures in power systems with high penetration of renewable energy.This paper also provides an analysis method for the choice of different protection and control measures at each stage of cascading failure,which has critical significance and follow-up value.

谈寒湿疫之寒湿入营

仝小林院士提出新型冠状病毒感染属寒湿疫,其病理因素为寒湿,应从散寒化湿而治。寒湿入营是寒湿疫特殊证型,见于危重阶段,其病因病机及辨治施治均不同于热入营分。从寒湿入营的特点及鉴别角度进一步梳理、更新、完善寒湿疫辨证理论体系,诠释寒湿入营理论的临床意义,以期为寒湿疫危重症防治提供新思路。

中国古代饮酒辟疫民俗的中医学阐释

饮酒辟疫是中国古代的传统民俗现象,也是古人防治疫病的智慧结晶。酒是辟疫酒方的重要组成部分,其辛热透散之效可助行药势,通脉厚肠之功能养脾扶肝。古代辟疫酒方主要包括屠苏酒、椒柏酒、豉术酒及松毛酒。酒与诸药配伍,以顾护正气为主,未病先防;祛邪外出的同时注意调达气机,祛邪不伤正,寓治于防。屠苏酒与椒柏酒“正月正旦,东向饮”的饮用方式还与中医学春日肝主升发的理论相应,体现了顺应四时、天人相应的整体观。

《温病条辨》霹雳散方证探析

霹雳散见于《温病条辨》,其制方特色、学术渊源、临床应用、同名方剂等未见系统性地考察。霹雳散同名方剂用于外感热病、妇科崩漏、内科癫狂、温病中燥、痢疾痧霍、中恶惊风6种病证。《温病条辨》霹雳散是针对1821年顺天真性霍乱大流行而设,主治寒湿伤阳之证。其理论基础为吴鞠通秋燥胜复学说,主治病证有燥极似泽、吐泻厥痛的特点,其制方具有苦热刚燥、芳香逐秽的鲜明特色。该方丰富了中医治疗燥疫、寒湿疫一类疾病的辨治经验,与秋燥胜复学说一起拓展了中医燥淫致病的理论体系。

从温病“先入后出,从阴引阳”理论探讨达原饮类方的中医思维

达原饮为明末清初医家吴又可首创,在瘟疫盛行之时,其影响范围遍布全国,吴又可在总结大量临床经验教训的基础上,创《温疫论》一书,其中达原饮可称众方之首。后世温病学派如叶天士、吴鞠通、王孟英、薛生白、雷少逸、俞根初等众多医家,灵活变通,对达原饮有不同程度的继承和创新。本文通过分析达原饮及其变方的用药逻辑,以此为例提出温病学派用药规律的创新性认知,即“先入后出”、“从阴引阳”为主的用药理论。