一类空间非齐次的SIR传染病模型的稳态解

为研究环境的空间异质性和种群扩散对传染病持续和消除的影响,本文提出了一类空间非齐次的SIR传染病模型．首先,构造模型的基本再生数$R_{0}$,并分析染病者的扩散对$R_{0}$的影响．若$R_{0}<1$,则无病平衡点全局渐近稳定;若$R_{0}>1$,则无病平衡点不稳定．其次,在低危险区域,我们运用分歧理论研究了地方病平衡点的存在性和稳定性．结果表明,减少染病者的扩散并不有利于传染病的消除,但地方病平衡点的不稳定性表明最终传染病可以得到控制．     

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

本文对一类具有非线性发生率的SEIR传染病模型进行了研究．确定了决定疾病灭绝或持续存在的阈值-基本再生数,并分析了模型的平衡点的存在性;通过构造恰当的Lyapunov函数,运用LaSalle不变性原理证明了当基本再生数小于或等于1时,无病平衡点是全局渐进稳定的;利用Lyapunov直接方法证明了当基本再生数大于1时,地方病平衡点是全局渐进稳定的．最后,将发生率具体化用数值模拟验证了所得理论分析结果的正确性．     

一类具有Beverton-Holt出生函数的阶段结构传染病模型的全局分析

针对一些疾病仅在成年个体间传播和成年个体的成长受到密度制约等因素,建立了一类具有幼年和成年两个阶段且疾病仅在成年个体间传播的传染病模型,其中以具有饱和性质的Beverton-Holt函数作为幼年出生函数．通过构造恰当的Lyapunov函数和定性分析,得到了模型的全局动力学性态,并确定了决定模型动力学性态的种群存活的基本再生数和疾病传播的基本再生数．所得结果表明：当种群的基本再生数不大于 1 时,种群灭绝;当种群的基本再生数大于 1 而疾病传播的基本再生数不大于 1 时,种群持续生存而疾病灭绝;当疾病传播的基本再生数大于 1 时,种群持续存活且疾病会发展成地方病．     

一类具有阶段结构的传染病模型的全局分析

考虑疾病仅在成年个体间传播,并且成年个体的增长受到密度制约,本文建立了一类具有双线性发生率和阶段结构的传染病模型．文中得到了种群增长的基本再生数和疾病传播的基本再生数,通过构造Lyapunov函数证明了平衡点的全局稳定性,通过数值模拟验证了所获得的结果．结果显示,两类基本再生数完全确定了模型的动力学性态,通过降低传染率和增大染病者移除率可以降低疾病基本再生数．     

带时滞的传染病模型的全局稳定性

研究了一类SEIS传染病模型的全局稳定性,通过构造Liapunov泛函,证明了当潜伏期较小,染病期较长并且再生数接近于1时,该模型的地方病平衡点是全局渐近稳定的。     

基于Beverton-Holt出生函数的阶段结构传染病模型的稳定性和分支北大核心CSCD

基于Beverton-Holt出生函数,考虑疾病仅在成年个体间传播且患病成年个体具有一定出生率等因素,建立了一类具有幼年和成年两个阶段的传染病模型。分析了模型平衡点的存在性,通过构造恰当的Lyapunov函数和定性分析,得到了模型平衡点的稳定性,并确定了模型出现后向分支的条件。最后,借助数值模拟验证了所得分析结果的正确性。     

具有抗体反应的HBV/HCV传染病模型的全局性态分析

本文建立了在肝脏和血液中存在乙肝病毒(HBV)或丙肝病毒(HCV)的数学模型,并且考虑了抗体的作用。得到了两个阈值参数R01和R02,它们决定了HBV/HCV感染和抗体反应的持续性和绝灭性。结果表明,当R01<1时,病毒最终被清除,抗体反应消失;当R02<11,病毒和抗体反应最终在宿主中持续。     

The pluses and minuses of R0.

The concept of the basic reproduction number (R0) occupies a central place in epidemic theory. The value of R0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if R0>1, (ii) the value of R0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of R0. These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.     

On the predictive ability of mechanistic models for the Haitian cholera epidemic

Predictive models of epidemic cholera need to resolve at suitable aggregation levels spatial data pertaining to local communities, epidemiological records, hydrologic drivers, waterways, patterns of human mobility and proxies of exposure rates. We address the above issue in a formal model comparison framework and provide a quantitative assessment of the explanatory and predictive abilities of various model settings with different spatial aggregation levels and coupling mechanisms. Reference is made to records of the recent Haiti cholera epidemics. Our intensive computations and objective model comparisons show that spatially explicit models accounting for spatial connections have better explanatory power than spatially disconnected ones for short-to-intermediate calibration windows, while parsimonious, spatially disconnected models perform better with long training sets. On average, spatially connected models show better predictive ability than disconnected ones. We suggest limits and validity of the various approaches and discuss the pathway towards the development of case-specific predictive tools in the context of emergency management.     

Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: scenarios for the US, UK and the Netherlands

An increasing number of avian flu cases in humans, arising primarily from direct contact with poultry, in several regions of the world have prompted the urgency to develop pandemic preparedness plans worldwide. Leading recommendations in these plans include basic public health control measures for minimizing transmission in hospitals and communities, the use of antiviral drugs and vaccination. This paper presents a mathematical model for the evaluation of the pandemic flu preparedness plans of the United States (US), the United Kingdom (UK) and the Netherlands. The model is used to assess single and combined interventions. Using data from the US, we show that hospital and community transmission control measures alone can be highly effective in reducing the impact of a potential flu pandemic. We further show that while the use of antivirals alone could lead to very significant reductions in the burden of a pandemic, the combination of transmission control measures, antivirals and vaccine gives the most 'optimal' result. However, implementing such an optimal strategy at the onset of a pandemic may not be realistic. Thus, it is important to consider other plausible alternatives. An optimal preparedness plan is largely dependent on the availability of resources; hence, it is country-specific. We show that countries with limited antiviral stockpiles should emphasize their use therapeutically (rather than prophylactically). However, countries with large antiviral stockpiles can achieve greater reductions in disease burden by implementing them both prophylactically and therapeutically. This study promotes alternative strategies that may be feasible and attainable for the US, UK and the Netherlands. It emphasizes the role of hospital and community transmission control measures in addition to the timely administration of antiviral treatment in reducing the burden of a flu pandemic. The latter is consistent with the preparedness plans of the UK and the Netherlands. Our results indicate that for low efficacy and coverage levels of antivirals and vaccine, the use of a vaccine leads to the greatest reduction in morbidity and mortality compared with the singular use of antivirals. However, as these efficacy and coverage levels are increased, the use of antivirals is more effective.     

总人口在变化的SIR流行病模型

考虑了具有连续预防接种的SIR流行病模型,在连续预防接种下,分析了平衡点的存在性及其稳定性,并给出了SIR流行病模型基本再生数。     

相邻场群上有迁移的动物疫病传播模型分析

本文主要研究不同距离场群之间疫病的交叉感染和动物的迁移对动物疫病传播的影响．首先,根据疫病的传播基理,建立了相邻场群上有动物迁移的一类动物疫病传播模型．其次,利用微分方程定性稳定性理论,讨论了系统无病平衡点和地方病平衡点的存在性,证明了系统的无病平衡点是全局渐近稳定的．最后,对结果进行数值分析,定量分析了基本再生数对于不同参数的敏感性．结果表明,个体与环境细菌的接触传染系数以及个体从非相邻场群的迁入系数对基本再生数的影响较大．     

Next-generation tools for evolutionary invasion analyses

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such ‘invasion fitness’ expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called ‘next-generation’ matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.     

一类具有垂直传播的HIV模型的稳定性分析

根据艾滋病的传播规律,本文建立了一类传染病模型.在模型中,HIV携带者分为幼年和成年两类,HIV可垂直传染,艾滋病患者有额外死亡.我们用再生矩阵求出了模型的基本再生数,并得出当基本再生数小于1时,模型只有无病平衡点,而当基本再生数大于1时,模型还有地方病平衡点.最后,应用第二加性复合矩阵等理论,文中证明了各平衡点全局渐近稳定性.     

基于危险网络上的吸毒人群中HIV的传播(英文)

通过建立吸毒人群中交往关系(包括针具共用和性关系)的"危险关系网络",我们研究了一个关于HIV在此人群中传播的随机模型,得到了基本再生数和最终感染者比例。使用四川省西昌市的调查数据,我们研究了针具共用以及性关系的网络规模对模型最终结果的影响。模拟发现,每个注射吸毒者每增加一个"三人小圈子"网络,将最终导致增加10%的感染者。结果提示:减少危险关系网络的规模,尤其是针具共用的网络规模,对控制HIV的传播有重要的作用。     

具有季节性反应扩散疟疾模型的全局动力学

疟疾是一种由疟原虫引起的传染病,它是通过成年雌性按蚊叮咬而引发的人与人之间传播.为了探讨空间异质和季节性对疟疾传播的影响,建立了一类周期的反应扩散模型.鉴于蚊子总密度趋于一个正的周期解,故对原系统的研究转而讨论其极限系统.首先定义了模型的基本再生数R0,然后利用单调次齐性系统理论表明了R0是决定极限系统全局动力学的一个阈值参数.具体地说,当R0 ≤ 1时,无病周期解是全局渐近稳定的;而当R0＞1时,模型存在唯一正的周期解且它是全局渐近稳定的.最后,利用链传递集理论将极限系统的动力学提升到原系统.