一类非自治SIRS传染病模型的持久性与灭绝性研究

本文研究了一类非自治SIRS传染病模型．在比较弱的条件下,我们不仅得到了疾病强一致持续的充分必要条件,还证明了疾病强一致持续与强持续的等价性．本文给出了新的闽值．另外也给出了疾病灭绝的条件．文献[7]中的结论被改进．     

多种群阶段结构竞争系统的周期解与概周期解

研究具有阶段结构的多种群竞争系统,得到该系统一致持久,正周期解全局渐近稳定及概周期解的存在性与一致渐近稳定性的充分条件。     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.     

Patterns and propensities in reproduction and growth of marine fishes

A number of strong regularities characterize certain very basic biological parameters in marine fishes. For example, the ovulated eggs of fish usually measure approximately 1 mm in diameter. The small, relatively uniform size of the eggs means that almost all fish larvae experience environmental variability at very similar scales, which itself establishes strong constraints for, and links between reproduction and recruitment. Additional constraints emerge from seawater being a poor medium for respiration, which establishes further linkages between growth and mortality. These constraints have produced strongly convergent features, and thence the patterns in reproduction and growth of marine fishes that are presented.     

Global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays

This paper addresses the global existence and global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays. By using a novel approach, sufficient conditions are derived for the existence and global exponential convergence of positive solutions of the model without any restriction on uniform positiveness of the per capita dead rate. Numerical examples are provided to illustrate the effectiveness of the obtained results.     

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.     

A Periodic Droop Model for Two Species Competition in A Chemostat

Both uniform persistence and the existence of periodic coexistence state are established for a periodically forced Droop model on two phytoplankton species competition in a chemostat under some appropriate conditions. Numerical simulations using biological data are presented as well to illustrate the main result. Research supported in part by the NSERC of Canada and the MITACS of Canada.     

榕-传粉榕小蜂间的专一性与协同进化

共生体系的长期维持引发了一系列进化问题, 特别是共生双方的相互适应、协同进化成为进化理论的一大挑战。榕和传粉榕小蜂是目前所知的专性最强的共生体系之一, 两者异常丰富的物种组成以及宿主多样的生活型为以上问题的研究提供了理想的体系。早期认为榕与其传粉小蜂间均为狭义协同进化, 一对一原则在该体系中具有普适性。然而近年来发现越来越多的例外, 特别是宿主转移现象在某些地区、某些榕属类群中的普遍存在, 使榕及其传粉小蜂间严格的物种专一性及协同进化发生在物种水平的观点受到质疑, 最近提出了一个新的协同进化模式来解释榕与其传粉小蜂的对应关系。榕与传粉小蜂间的进化模式说明两者间既有狭义的协同进化, 也有发散协同进化关系, 从而导致它们之间物种专一性不同。目前, 两种协同进化模式在该系统中的相对重要性仍存在很大争议, 不同地区、不同榕属类群中两者的物种专一性程度和产生原因可能有很大差异, 榕与传粉榕小蜂系统的复杂性决定了不能将某些地区和某些类群的结论简单扩展, 有关该体系协同进化主导模式的正确评判有待于对不同地区和不同榕属类群对应传粉小蜂的物种组成、来源方式, 以及共生双方的系统发生关系进行更广泛、更深入的研究。     

具有时滞的非自治差分竞争系统的渐近行为研究(英文)

提出了一个具有时滞的非自治差分竞争系统.分别利用差分不等式及Lyapunov离散函数技巧,得到了系统永久持续生存和正解全局吸引的充分条件.数值模拟验证了理论结果的正确性.     

Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment

We investigate the persistence of a mosquito-borne disease (malaria) in a system where mosquitoes and hosts are grouped in patches containing any number of individuals. A mosquito from any one of vector patches can bite, and take blood meals, in any one of m host patches. We confirm our earlier result (C. Dye and G. Hasibeder, 1986, Trans. R. Soc. Trop. Med. Hyg. 80, 69-77) that nonhomogeneous host selection by mosquitoes leads to basic reproductive rates (which measure the persistence of infection in the system) greater than or equal to those obtained under uniform host selection. We find, in addition, that strong associations between particular groups of mosquitoes and hosts lead to still higher basic reproductive rates. Exacting fieldwork would be required to find out how much higher.     

The E1 ubiquitin-activating enzyme Uba1 in Drosophila controls apoptosis autonomously and tissue growth non-autonomously

Ubiquitination is an essential process regulating turnover of proteins for basic cellular processes such as the cell cycle and cell death (apoptosis). Ubiquitination is initiated by ubiquitin-activating enzymes (E1), which activate and transfer ubiquitin to ubiquitin-conjugating enzymes (E2). Conjugation of target proteins with ubiquitin is then mediated by ubiquitin ligases (E3). Ubiquitination has been well characterized using mammalian cell lines and yeast genetics. However, the consequences of partial or complete loss of ubiquitin conjugation in a multi-cellular organism are not well understood. Here, we report the characterization of Uba1, the only E1 in Drosophila. We found that weak and strong Uba1 alleles behave genetically differently with sometimes opposing phenotypes. Whereas weak Uba1 alleles protect cells from cell death, clones of strong Uba1 alleles are highly apoptotic. Strong Uba1 alleles cause cell cycle arrest which correlates with failure to reduce cyclin levels. Surprisingly, clones of strong Uba1 mutants stimulate neighboring wild-type tissue to undergo cell division in a non-autonomous manner giving rise to overgrowth phenotypes of the mosaic fly. We demonstrate that the non-autonomous overgrowth is caused by failure to downregulate Notch signaling in Uba1 mutant clones. In summary, the phenotypic analysis of Uba1 demonstrates that impaired ubiquitin conjugation has significant consequences for the organism, and may implicate Uba1 as a tumor suppressor gene.     

一类具有饱和反应率的脉冲免疫接种的SIS模型

研究了具饱和传染率的脉冲免疫接种SIS模型,得到了无病周期解全局渐近稳定的充分条件和系统持续生存的充分条件．     

具有庇护所的三种群捕食者-食饵模型

讨论了一类具有庇护所的自治三种群捕食者一食饵模型,运用Liapunov函数方法,得到了该模型持久性的充分条件．对于该模型的周期系统,在一定的条件下,将产生唯一一个全局渐近稳定的周期正解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定性的充分条件．     

Dynamical analysis of periodic bursting in piece-wise linear planar neuron model

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.     

污染环境下单种群模型生存阈值

本论文研究了污染环境下毒素对单种群生存的影响。在环境容纳量较小的假设下建立了生物种群模型,在该模型中不但考虑了环境毒素浓度对生物个体生存的影响,还考虑了生物个体从食物链中吸收的毒素对其影响。通过研究得到种群一致持续生存和若平均持续生存的充分条件,同时得到种群持续生存依赖于模型参数和生物个体体内毒素净化率的某些充分条件．     

Common and Distinct Genetic Properties of ESCRT-II Components in Drosophila

Background

Genetic studies in yeast have identified class E vps genes that form the ESCRT complexes required for protein sorting at the early endosome. In Drosophila, mutations of the ESCRT-II component vps25 cause endosomal defects leading to accumulation of Notch protein and increased Notch pathway activity. These endosomal and signaling defects are thought to account for several phenotypes. Depending on the developmental context, two different types of overgrowth can be detected. Tissue predominantly mutant for vps25 displays neoplastic tumor characteristics. In contrast, vps25 mutant clones in a wild-type background trigger hyperplastic overgrowth in a non-autonomous manner. In addition, vps25 mutant clones also promote apoptotic resistance in a non-autonomous manner.

Principal Findings

Here, we genetically characterize the remaining ESCRT-II components vps22 and vps36. Like vps25, mutants of vps22 and vps36 display endosomal defects, accumulate Notch protein and – when the tissue is predominantly mutant – show neoplastic tumor characteristics. However, despite these common phenotypes, they have distinct non-autonomous phenotypes. While vps22 mutations cause strong non-autonomous overgrowth, they do not affect apoptotic resistance. In contrast, vps36 mutations increase apoptotic resistance, but have little effect on non-autonomous proliferation. Further characterization reveals that although all ESCRT-II mutants accumulate Notch protein, only vps22 and vps25 mutations trigger Notch activity.

Conclusions/Significance

The ESCRT-II components vps22, vps25 and vps36 display common and distinct genetic properties. Our data redefine the role of Notch for hyperplastic and neoplastic overgrowth in these mutants. While Notch is required for hyperplastic growth, it appears to be dispensable for neoplastic transformation.     

Enzyme adsorption in porous supports: local thermodynamic equilibrium model

Enzyme adsorption from a finite bath (batch adsorption) onto porous spherical supports is investigated both experimentally and theoretically using beta-galactosidase and Duolite ion-exchange resin as a model system. Efficient numerical techniques are presented that have been used in conjunction with a parameter estimation routine to evaluate adsorption isotherm constants. Results show that even for adsorption processes lasting almost 10 h, the majority of the enzyme is confined to the outer half of the support and, for high initial enzyme concentrations in the bath, this loading takes place as a slowly moving front. Information on the enzyme distribution has practical importance in the design of immobilized enzyme reactors that in previous works have almost always been analyzed assuming a uniform catalyst distribution.     

Survival Analysis of Stochastic Competitive Models in a Polluted Environment and Stochastic Competitive Exclusion Principle

Stochastic competitive models with pollution and without pollution are proposed and studied. For the first system with pollution, sufficient criteria for extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean, and stochastic permanence are established. The threshold between weak persistence in the mean and extinction for each population is obtained. It is found that stochastic disturbance is favorable for the survival of one species and is unfavorable for the survival of the other species. For the second system with pollution, sufficient conditions for extinction and weak persistence are obtained. For the model without pollution, a partial stochastic competitive exclusion principle is derived.