具有潜伏和隔离的传染病模型的全局稳定性

研究了一类具有隔离仓室和潜伏仓室的非线性高维自治微分系统SEQIJR传染病模型,得到疾病绝灭与否的阀值一基本再生数R0．证明了当R0≤1时,模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的,疾病最终绝灭;当R0〉1时,模型存在两个平衡点,无病平衡点不稳定,地方病平衡点全局渐近稳定,疾病将持续．隔离措施影响着基本再生数,进而推得结论：适当地增大隔离强度,将有益于有效地控制疾病的蔓延．这就从理论上揭示了隔离对疾病控制的积极作用．     

湿地中的藻类生态学研究进展

从湿地中藻类的种群结构、藻类在湿地中的功能、湿地中的藻类生产力及其影响因素等方面综述了天然湿地中的藻类生态学研究进展．湿地植物区系主要有附泥藻类、附植藻类、后周丛藻类和浮游植物4种类型,其中常见的是附泥藻类的硅藻、绿藻和蓝藻．藻类最显著的作用是作为湿地食物网中的初级生产者,也作为湿地环境污染的生物指示物．影响藻类生产力的因素有水力学因素、营养、温度、光、大型植物及草食动物和其它动物．未来对藻类的研究应侧重于湿地藻类生物多样性、藻类生物量、生产力、种群组成的环境控制及其相互关系,以及藻类作为水环境及湿地污染程度指标的研究,“基因治藻”也将是未来研究的新方向．     

一具有非线性发生率传染病模型的稳定性和霍普夫分支

在这篇文章中,我们研究了一具有非线性发生率的传染病模型．该模型经历了鞍结点分支和霍普夫分支．我们对模型的霍普夫分支进行了详细的分析,得知该霍普夫分支是超临界的．此外,我们给出了支持理论分析的数值模拟．     

具有非线性接触率的SILI流行病模型

本文研究了具有一般非线性接触率的SILI流行病模型的平衡点的存在性、稳定性以及Hopf分支现象,并且分析了潜伏期的时滞效应．     

一类具有脉冲投放鱼类的淡水生态系统模型

将氮、藻类和鱼类分别作为淡水生态系统的营养物质、生产者和消费者的代表,考虑投放鱼类以控制水华发生的管理措施,建立了一类具有脉冲投放的淡水生态系统模型.利用Floquet理论等研究了边界周期解的存在性和稳定性,最后给出了相关生物意义.     

一类具有功能反应的生物捕食系统的脉冲控制

研究了一类具有功能反应的捕食一被捕食生物模型x1=x1g(x1)-x2φ（x1),x2=x2(-d eφ(x1))在g(x)和φ（x）都非线性情形下,加以脉冲控制△X=BkX之后的稳定性问题．     

具有阶段结构和非线性接触率的SI传染病模型的渐近性态

研究了一类具有阶段结构和非线性接触率的传染病模型的渐近性态,得到了传染病最终消除和成为地方病的阀值．     

程海富营养化机理的神经网络模拟及响应情景分析

揭示湖泊的富营养化发生机制、定量了解关键生源要素与藻类爆发的因果关联对有效改善湖泊水质和富营养化状况具有重要的科学与决策意义。本研究以云南省程海为例,建立了基于神经网络的响应模型,对富营养化机理进行了研究,并从富营养化核心驱动因子识别、神经网络模型构建与架构分析以及叶绿素a(Chl a)与TN、TP浓度降低的响应模拟几个方面对面临的科学问题进行探索。模拟结果表明,神经网络模型必须在适当的架构下才能产生科学合理的结果;程海的富营养化机制由一个氮(N)、磷(P)共限制的营养盐-藻类动力结构主导,但在此主导结构下拥有氮型限制的次级结构。基于神经网络模型模拟,推导出一系列基于湖体水质控制的Chl a响应的非线性函数,为程海的富营养化控制提供了快速决策支持。     

小球藻病毒的分离

真核藻类作为一类重要的淡水和海洋水生生物与人类和环境有密切关系。在生态学上,藻类作为普通食物链中的原初生产者,在水环境中显得尤为重要,可作为许多水生生物的食物,也可使水域在一定范围内自净。藻类还极有希望成为人类新的食物来源和能源。但藻类的过量繁殖可引起严重的水污染。因此,搞清真核藻类与其寄生物—真核藻类病毒的关系,对维持藻类的生态平衡,控制利用藻类资源意义重大。对真核藻类病毒的深入研究已揭示出这类病毒在自然界的广泛存在。到目前为止,已报道发现的真核藻类病毒或病毒状颗粒(Virus—like particle)至少有44种,但多数仅限于电镜观察。直到病毒裂解性小球藻的发现,才使得对真核藻类病毒的研究提高到一个新水平,也使该领域的研究越来越受到人们的关注,国际上已开展真核藻类病毒研究的国家有美国、日本,德国等,我国在该领域的研究尚属空白。在国内开展真核藻类病毒的研究,首先要深入地调查我国的真核藻类病毒资源,同时可阐明一类新的病毒——寄主关系的分子生物学基础,了解诸如病毒基因组在寄主细胞中的表达调控,为研究高等植物基因的表达调控提供一个适宜的模型。另外,由于已知的真核藻类病毒具有相当大的基因组,可预见其基因…     

轮叶黑藻浸提液对蓝藻水华的抑制作用

探讨了大型沉水植物轮叶黑藻[Hydrilla verticillata（Linn．f）]浸提液对铜绿微囊藻（Microcystis aeruginosa）以及池塘混合藻类的抑制作用。结果表明：轮叶黑藻浸提液不仅对铜绿微囊藻有明显的抑制作用,而且对池塘复合藻类也有不同程度的抑制作用。该项研究不仅培养了学生的科研创新能力,系统地掌握了藻细胞的培养、显微镜的使用、藻细胞的计数、叶绿素a含量的测定等方法．而且对于蓝藻水华的预防控制还具有较重要的理论与应用意义。     

Nonlinear control for algae growth models in the chemostat

This paper deals with output feedback control of phytoplanktonic algae growth models in the chemostat. The considered class of model is of variable yield type, meaning that the ratio between the environmental nutrient absorption rate and the cells’ growth rate varies, which is different from classical bioprocesses assumptions. On the basis of weak qualitative hypotheses on the analytical expressions of the involved biological phenomena (which guarantee robustness of the procedure toward modeling uncertainties) we propose a nonlinear controller and prove its ability to globally stabilize such processes. Finally, we illustrate our approach with numerical simulations and show its benefits for biological laboratory experiments, especially for ensuring persistence of the culture facing classical experimental problems.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Steady-state rotifer growth in a two-stage, computer-controlled turbidostat

Steady-state populations of rotifers (Brachionus calyciflorus)were maintained in twostage, continuous-flow turbidostatic cultureon the green alga Chlorella pyrenoidosa. In this system, themaximum specific growth rate,µ^max of the rotifers wasmaintained by using a computer to control the concentrationof algae, as rotifer food, in the rotifer culture. As rotifersconsumed algae, the turbidity decreased until a set-point wasreached. Then fresh algal suspension (supplied from a steady-statealgal chemostat) was metered into the rotifer culture, whichwas held in the dark. Rotifer and algal populations, as wellas rotifer µ^max entered steady states. These steady-stateresults were consistent with previous data from chemostat studies,but growth transients indicated that the of the µ^maxrotifersmay be subject to selection. The system is unique in providinga means to explore population dynamics of a metazoan maintainednear its µ^max.     

The attractiveness of the Droop equations.

The Droop equations are a system of three coupled, nonlinear ordinary differential equations describing the growth of a microorganism in a chemostat. The growth rate of the organism is limited by the availability of a single nutrient. In contrast to the better known Monod equations, the nutrient is divided into external and internal cellular pools. Only the internal pool can catalyze growth. This paper proves that the Droop equations are globally stable. Based on a single combination of parameters, either the chemostat organism goes extinct or it tends to a fixed, positive concentration.     

The use of carbonate equilibrium chemistry in quantifying algal carbon uptake kinetics

Summary The method of utilizing the principles of carbonate equilibrium chemistry to monitor the rate of inorganic carbon uptake by a variety of algal species is presented and discussed. The usefulness of this technique is demonstrated for both batch and chemostat algal culture. Data obtained from carbon limited batch and chemostat cultures suggest that the specific growth rate of a variety of algal species may best be represented as a Monod response to the free carbon dioxide concentration. The monitoring of carbonate equilibrium in the batch method provides a simple, rapid and inexpensive technique for obtaining rates of algal carbon fixation. This technique is well suited for obtaining the large volumes of detailed kinetic data necessary in building a basis for understanding the factors involved in algal productivity and algae species shifts, in both controlled and natural aquatic ecosystems.     

On the use of the logistic equation in models of food chains

In food chain models the lowest trophic level is often assumed to grow logistically. Anomalous behaviour of the solution of the logistic equation and problems with the introduction of mortality have recently been reported. As predation on the lowest trophic level is a kind of mortality, one expects problems with these food chain models. In this paper we compare two formulations for the lowest trophic level: the logistic growth formulation and the mass balance formulation with resources modelled explicitly. We examine the effects of both models on the dynamic behaviour of a tri-trophic microbial food chain in a chemostat. For this purpose bifurcation diagrams, which give the existence and stability of the equilibria of the nonlinear dynamic system, are used. It turns out that the dynamic behaviours differ in a rather large region of the control parameter space spanned by the dilution rate and the concentration of the resources in the reservoir. We urge that mass balance equations should be used in modelling food chains in chemostats as well as in ecosystems.     

Feedback identification of continuous microbial growth systems

The fundamental problem of dynamic modeling of continuous culture systems for process control and optimization is addressed. Forcing a system to bifurcation via feedback control is a very promising method for model discrimination and identification. Dynamic information is obtained by using this technique, the dynamic behavior of the chemostat as predicted by unstructured models, the model with delay, and a structured model has been analyzed. The method exposes significant differences in the nonlinear dynamic structure of the various models and can be implemented to discriminate between various possible models for a continuous culture system.     

Delayed feedback control for a chemostat model

In this paper, we discuss asymptotic properties and numerical simulations of a chemostat model with delayed feedback control. A chemostat model with two organisms can be made coexistent by feedback control of the dilution rate which depends affinely on the concentrations of two organisms [P. De Leenher, H.L. Smith, Feedback control for chemostat models, J. Math. Biol. 46 (2003) 48]. Then the coexistence takes its simplest form; the equilibrium point in the non-negative orthant is globally asymptotically stable. We show that stability of the equilibrium point is changed by 'time-delay' caused in controlling the dilution rate after measuring the concentrations of two organisms.     

The periodically forced Droop model for phytoplankton growth in a chemostat

 It is proved that the periodically forced Droop model for phytoplankton growth in a chemostat has precisely two dynamic regimes depending on a threshold condition involving the dilution rate. If the dilution rate is such that the sub-threshold condition holds, the phytoplankton population is washed out of the chemostat. If the super-threshold condition holds, then there is a unique periodic solution, having the same period as the forcing, characterized by the presence of the phytoplankton population, to which all solutions approach asymptotically. Furthermore, this result holds for a general class of models with monotone growth rate and monotone uptake rate, the latter possibly depending on the cell quota. Received 10 October 1995; received in revised form 26 March 1996     

A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

When the growth of bacteria in a chemostat is controlled by limiting the supply of a single essential nutrient, the growth rate is affected both by the concentration of this nutrient in the culture medium and by the amount of time that it takes for the chemical and physiological processes that result in the production of new biomass. Thus, although the uptake of nutrient by cells is an essentially instantaneous process, the addition of new biomass is delayed by the amount of time that it takes to metabolize the nutrient. Mathematical models that incorporate this "delayed growth response" (DGR) phenomenon have been developed and analysed. However, because they are formulated in terms of parameters that are difficult to measure directly, these models are of limited value to experimentalists. In this paper, we introduce a DGR model that is formulated in terms of measurable parameters. In addition, we provide for this model a complete set of criteria for determining persistence versus extinction of the bacterial culture in the chemostat. Specifically, we show that DGR plays a role in determining persistence versus extinction only under certain ranges of chemostat operating parameters. It is also shown, however, that DGR plays a role in determining the steady-state nutrient and bacteria concentrations in all instances of persistence. The steady state and transient behavior of solutions of our model is found to be in agreement with data that we obtained in growing Escherichia coli 23716 in a chemostat with glucose as a limiting nutrient. One of the theoretical predictions of our model that does not occur in other DGR models is that under certain conditions a large delay in growth response might actually have a positive effect on the bacteria's ability to persist.