一个竞争模型的一致持续生存

本文研究一个带有时滞的竞争模型的一致持续生存。首先证明了离散时滞不影响种群的一致持续生存,接着在种群增长率是周期的假设下讨论了正周期解的存在性,最后给出了连续时滞模型一致持续生存的充分条件。     

污染环境中Leslie系统的生存分析

研究环境污染对Ｌｅｓｌｉｅ资源－消费者系统中消费者种群的长期影响,给出了种群弱持续生存和绝灭的条件,在一定条件下得到了阈值．     

静脉注射吸毒人群HIV／AIDS数学模型分析

建立了四川省西昌市静脉注射吸毒人群HIV／AIDS传播的数学模型,给出了模型的理论分析和数值模拟结果．通过必要的分析,给出了各类平衡点的存在性和稳定性,系统的一致持续生存,以及基本再生数的数学表达式和具体取值．揭示了该静注人群中的HIV／AIDS有进一步蔓延的趋势,但如果采取适当的干预措施,该静注人群中HIV／AIDS流行可得到有效的控制．     

一类具阶段结构的捕食者-食饵模型的渐进性质

研究了一类具阶段结构的捕食者-食饵模型的渐近性质．文中假设由幼年阶段转化为成年阶段的转化率依赖于幼年个体数量．建立了捕食种群一致持续生存与绝灭的条件．证明了稳定的周期解的存在性．     

Leslie系统在污染环境下有关生存问题的分析

研究了在污染环境中毒素对Leslie资源-消费者系统中消费者种群的长期影响,给出了种群弱持续生存和灭绝的条件．     

具污染与捕获的Logistic单种群的持续生存及绝灭

当今社会工农业的高速发展在给人们带来经济利益的同时,也造成了严重的环境污染．一些生物种群一方面受到污染的威胁,另一方面还要满足人们捕获的需求．这就使得环境污染中的种群捕获问题成为人们关心的问题．本文指出以往环境污染单种群模型的不足之处,基于文献[3]的基础上给出新模型;并得到了一致持续生存及灭绝的充分条件;而且通过具体例子给出两个控制变量：环境毒素输入率和捕获率之间的关系图．     

防护措施下一类高传染性多潜伏期传染病的高维动态模型

传染病给人们的生命带来了极大的威胁,对于高传染性的疾病,政府总会采取一些防护措施．本文针对防护措施下的高传染性且具有潜伏期等特性的一类传染病,结合传染病模型,在一定假设条件下给出了这类疾病单日新收治的直接确诊病例及疑似病例的高维动态模型,并使用最小二乘法进行了参数辨识．最后以SARS为例,利用网上公布的SARS数据给出了5月22日-5月31日的预测结果并将预测结果和实际数据进行了比较,说明了模型的有效性．     

具有Holling Ⅲ类功能性反应的多种群竞争捕食系统全局稳定的条件

研究了具有HollingⅢ类功能性反应的非自治多种群竞争捕食生态系统所有参数都是时变的．证明了此系统在适当的条件下是一致持续生存的,进一步通过构造适当的Lyapunov函数,得到保证系统全局稳定周期解的充分性条件,     

污染环境中的Smith系统生存分析

研究了环境污染对Smith系统中种群生存的长期影响,考虑到种群数量的变化对种群个体体内毒素浓度和环境中毒素浓度的影响,对传统的Smith系统进行了修正,并且给出了一些种群弱平均持续生存和绝灭的充分条件．在一定条件下得到了弱平均持续生存与绝灭的阈值．     

具有垂直传染的时滞SEIR流行病模型分析

本文建立一类具有垂直传染的时滞SEIR流行病模型,得到了疾病流行与否的阈值条件,利用时滞微分方程的Lyapunov-Lasalle方法证明了当基本再生数R_0≤1时,无病平衡点E_0的全局渐近稳定性,此时疾病将会消失;当基本再生数R_01时,疾病将一致持续生存.     

A sharp threshold for disease persistence in host metapopulations

A sharp threshold is established that separates disease persistence from the extinction of small disease outbreaks in an S→E→I→R→S type metapopulation model. The travel rates between patches depend on disease prevalence. The threshold is formulated in terms of a basic replacement ratio (disease reproduction number), ?(0), and, equivalently, in terms of the spectral bound of a transmission and travel matrix. Since frequency-dependent (standard) incidence is assumed, the threshold results do not require knowledge of a disease-free equilibrium. As a trade-off, for ?(0)>1, only uniform weak disease persistence is shown in general, while uniform strong persistence is proved for the special case of constant recruitment of susceptibles into the patch populations. For ?(0)<1, Lyapunov's direct stability method shows that small disease outbreaks do not spread much and eventually die out.     

Emergence, spread, persistence and fade-out of sylvatic plague in Kazakhstan

Predicting the dynamics of zoonoses in wildlife is important not only for prevention of transmission to humans, but also for improving the general understanding of epidemiological processes. A large dataset on sylvatic plague in the Pre-Balkhash area of Kazakhstan (collected for surveillance purposes) provides a rare opportunity for detailed statistical modelling of an infectious disease. Previous work using these data has revealed a host abundance threshold for epizootics, and climatic influences on plague prevalence. Here, we present a model describing the local space-time dynamics of the disease at a spatial scale of 20 × 20 km(2) and a biannual temporal scale, distinguishing between invasion and persistence events. We used a Bayesian imputation method to account for uncertainties resulting from poor data in explanatory variables and response variables. Spatial autocorrelation in the data was accounted for in imputations and analyses through random effects. The results show (i) a clear effect of spatial transmission, (ii) a high probability of persistence compared with invasion, and (iii) a stronger influence of rodent abundance on invasion than on persistence. In particular, there was a substantial probability of persistence also at low host abundance.     

A note on persistence about structured population models

In this paper, we report some results on persistence in two structured population models: a chronic- age-structured epidemic model and an age-duration-structured epidemic model. Regarding these models, we observe that the system is uniformly strongly persistent, which means, roughly speaking, that the proportion of infected subpopulation is bounded away from 0 and the bound does not depend on the initial data after a sufficient long time, if the basic reproduction ratio is larger than one. We derive this by adopting Thieme's technique, which requires some conditions about positivity and compactness. Although the compactness condition is rather difficult to show in general infinite-dimensional function spaces, we can apply Fréchet-Kolmogorov L(1)-compactness criteria to our models. The two examples that we study illuminate a useful method to show persistence in structured population models.     

Structural sensitivity of grazing formulations in nutrient controlled plankton models

Summary Stability and persistence properties of a family of non-spatial plankton models, each differentiated by its herbivore grazing term, are analytically compared. The dynamic persistence function in the model is shown to operate uniformly even though stability configuration characteristics of the model may be topologically distinct. The persistence threshold for each model indicates that total nutrient is a fundamental biological control. In the parameter space, all of the models studied are structurally unstable; however, an important bifurcation mechanism associated with this instability governs persistence. While, topologically, model transfigurement through parameter modulation is non-continuous, the biological populations evolve in a continuous or a lower semicontinuous manner. A basic conclusion of the paper is that fundamental problems for these marine ecological models remain unresolved since each of the models is a structurally unstable system for a fixed dynamically persistent ecology.     

A note on persistence about structured population models

In this paper, we report some results on persistence in two structured population models: a chronic- age-structured epidemic model and an age-duration-structured epidemic model. Regarding these models, we observe that the system is uniformly strongly persistent, which means, roughly speaking, that the proportion of infected subpopulation is bounded away from 0 and the bound does not depend on the initial data after a sufficient long time, if the basic reproduction ratio is larger than one. We derive this by adopting Thieme's technique, which requires some conditions about positivity and compactness. Although the compactness condition is rather difficult to show in general infinite-dimensional function spaces, we can apply Fréchet–Kolmogorov L ¹-compactness criteria to our models. The two examples that we study illuminate a useful method to show persistence in structured population models.     

Network theory of glycosylation--etiologic and pathogenic implications of changes in IgG glycoform levels in autoimmunity.

It is now well established that glycoproteins are populations of individual glycoforms. While it has been inferred from in vitro experiments that the differential glycosylation of glycoproteins diversifies their function, evidence is lacking for such a role in vivo. Alterations in IgG glycosylation in both normal and disease states in vivo, however, provide strong evidence that glycosylation is not static and may be a highly regulated event. The large amount of data correlating disease activity and severity in autoimmune diseases which have a strong B cell component with changes in the incidence of IgG glycoforms, now suggest that glycoform population shifts may not be just a marker of disease activity, but may also contribute directly to disease persistence and pathogenesis.     

Fast and Slow dynamics of Malaria model with relapse

Two mathematical models of malaria with relapse are studied. When the vector population size is constant, complete analyses of the dynamics are conducted. The geometric singular perturbation theory is used to analyze the full dynamics. On the critical manifold, from next generation matrix method, we obtain the basic reproduction number. The global stability of disease-free equilibrium and the uniformly persistence of malaria have also been analyzed. While the vector population size is variable, the basic reproduction number and the stability of disease-free as well as the malaria-infected equilibrium have been obtained in a similar way. Some numerical simulations are also given.     

Remodeling is at the heart of chromatin

Chromatin modifications are integral elements of chromosome structure and its function and the vasculature depends on tissue-specific genome regulation for its development. A general concept for the de-regulation of chromatin modifications in cardiac and vascular disease is also emerging. The recognition that metabolic memory contributes to disease persistence highlights the benefit of early and aggressive treatment. As for the importance of memory, we do know that good metabolic control delays the onset of long-term diabetic complications. There are striking parallels between the timing of disease and the development of complications. Landmark multicenter clinical trials on diabetes patients have popularized the concept that glucose is also a demonstrable determinant for the development of complications, indicating the prolonged benefit of intensive therapy and the lasting damage of conventional therapy. Each cell type experiences thousands of modifications to the epigenome in response to environmental changes it is exposed to. Therefore, history is neither lost nor forgotten and previous experiences and exposure may form future memories. There is now a strong resurgence in research trying to understand gene-environment interactions and to determine what commits specific vascular cell types to specific memories. Recent insights show that cardiac gene expression is distinguished by specific chromatin remodeling events and histone modifications that are associated with heart disease.     

Refugia and connectivity sustain amphibian metapopulations afflicted by disease

Metapopulation persistence in fragmented landscapes depends on habitat patches that can support resilient local populations and sufficient connectivity between patches. Yet epidemiological theory for metapopulations has largely overlooked the capacity of particular patches to act as refuges from disease, and has suggested that connectivity can undermine persistence. Here, we show that relatively warm and saline wetlands are environmental refuges from chytridiomycosis for an endangered Australian frog, and act jointly with connectivity to sustain frog metapopulations. We coupled models of microclimate and infection probability to map chytrid prevalence, and demonstrate a strong negative relationship between chytrid prevalence and the persistence of frog populations. Simulations confirm that frog metapopulations are likely to go extinct when they lack environmental refuges from disease and lose connectivity between patches. This study demonstrates that environmental heterogeneity can mediate host–pathogen interactions in fragmented landscapes, and provides evidence that connectivity principally supports host metapopulations afflicted by facultative pathogens.