Host-pathogen interactions, insect outbreaks, and natural selection for disease resistance

The theory of insect population dynamics has shown that heterogeneity in natural-enemy attack rates is strongly stabilizing. We tested the usefulness of this theory for outbreaking insects, many of which are attacked by infectious pathogens. We measured heterogeneity among gypsy moth larvae in their risk of infection with a nucleopolyhedrovirus, which is effectively heterogeneity in the pathogen's attack rate. Our data show that heterogeneity in infection risk in this insect is so high that it leads to a stable equilibrium in the models, which is inconsistent with the outbreaks seen in North American gypsy moth populations. Our data further suggest that infection risk declines after epidemics, in turn suggesting that the model assumption of constant infection risk is incorrect. We therefore constructed an alternative model in which natural selection drives fluctuations in infection risk, leading to reductions after epidemics because of selection for resistance and increases after epidemics because of a cost of resistance. This model shows cycles even for high heterogeneity, and experiments confirm that infection risk is indeed heritable. The model is very general, and so we argue that natural selection for disease resistance may play a role in many insect outbreaks.     

Two fish species competition model with nonlinear interactions and equilibrium catches

Two species competition model is built up by assuming the hypothetical second order interactions in order to consider effects of exploitation on two competing fish species with non-linear interactions. Most important characteristic of this model, compared withLotka-Volterra type linear competition model, is that this model can possess multiple stable equilibrium points. Therefore there is a possibility that two species keeping the equilibrium state at one stable equilibrium point will be attracted to the other stable equilibrium point after a heavy perturbation. In this model reversible change of the fishing pressure does not always results in that of the equilibrium catch. In this sence MSY concept for single species can not be extended to this model. If there are multiple stable equilibrium points, the change of the dominant fish species, catastrophic and irreversible change of each equilibrium catch may be observed when the perturbation by the exploitation is added. This phenomenon immediately reminds us of the change of the dominant fish species between Japanese common mackerel and Pacific saury in the northwest Pacific Ocean. In case of the management of two competing fish species with nonlinear interactions, the consideration on the balance between the fishing pressure for each species may be as important as the decision on the catch limit for each species. MSY level for each species based on the single-species theory could be quite erroneous.     

General Mathematical Frame for Open or Closed Biomembranes (Part I): Equilibrium Theory and Geometrically Constraint Equation

This paper aims at constructing a general mathematical frame for the equilibrium theory of open or closed biomembranes. Based on the generalized potential functional, the equilibrium differential equation for open biomembrane (with free edge) or closed one (without boundary) is derived. The boundary conditions for open biomembranes are obtained. Besides, the geometrically constraint equation for the existence, formation and disintegration of open or closed biomembranes is revealed. The physical and biological meanings of the equilibrium differential equation and the geometrically constraint equation are discussed. Numerical simulation results for axisymmetric open biomembranes show the effectiveness and convenience of the present theory.     

一类Kolmogorov系统的动力性质

用定性分析的方法对一类Kolmogorov系统(dx)/(dt)=x(a_0-a_11x a_2x~(n-1)-a3x~n a_4xy~m),(dy)/(dt)=y(b_1x~n-b_2),进行了研究．讨论了系统平衡点的性态,给出了系统无闭轨的充分条件以及存在唯一稳定极限环的条件．包含并推广了文献[3]的相关结果．     

Behavioural analysis of two prey-two predator model

To deal with real-life diversity of our ecosystem, this paper analyzes two prey-two predator model including both Type-I and Type-II functional responses. The interior equilibrium point of the proposed model is calculated; and behaviour of the model around that point is studied. Local stability at an interior equilibrium point is discussed; and possibility of Hopf-bifurcation with probable direction is studied. A generalized form of the Poincaré-Bendixon criterion is applied to establish the sufficient conditions for global stability of the proposed model surrounding at an interior equilibrium point. Numerical simulations are also conducted in support of our work. Conclusions of our findings and some probable future directions are also included at the end.     

一类具有标准发生率的SIS型传染病模型的全局稳定性

研究一类具有标准发生率的SIS传染病模型,讨论了各类平衡点存在的条件;运用微分方程的定性理论,得到了无病平衡点E_1和地方病平衡点E_2的全局渐近稳定的充分条件.     

具有年龄结构的食蚜蝇-蚜虫捕食模型

现有的具有年龄结构的捕食-食饵模型总是假设只有成年捕食者捕食猎物,这与实际情况不符。建立了一个幼年捕食者捕食食饵的具有年龄结构的食蚜蝇-蚜虫模型,应用微分方程定性理论,讨论了系统平衡点及其稳定性:其中平衡点E1(0,0,0)为不稳定的;满足一定条件时,边界平衡点E2(K,0,0)及正平衡点E3(x*,y1*,y2*)为局部渐近稳定的;且应用一致持续生存理论得到了系统永久持续生存的条件,为有害生物综合治理提供了理论依据。     

一类食饵捕食系统的Hopf分岔及周期解的稳定性

首先建立了具有时滞的三种群食饵捕食模型,并研究了平衡点的存在性,接着应用规范化方法和中心流行定理研究了Hopf分岔以及分岔周期解的稳定性.并举例论证.     

一类具变时滞的模糊BAM神经网络的平衡点的指数稳定性(英文)

研究一类具变时滞的模糊BAM神经网络.利用拓扑度论和微分不等式,获得了该类网络平衡点的存在性、唯一性和全局指数稳定性的充分条件.一个例子用来解释本文获得的结果.     

Conformation in solution and dynamics of a structurally constrained linear insect kinin pentapeptide analogue

The preferred conformations of the active diuretic insect kinin pentapeptide analogue Phe-Phe-Aib-Trp-Gly-NH2 were studied using nmr spectroscopy and molecular modeling. Structure sets consistent with rotating frame nuclear Overhauser effect spectroscopy distance constraints obtained by restrained simulated annealing in vacuo indicate a predominant population of a type II beta-turn involving the Phe1-Trp4 region. An equilibrium between this type II and a type I beta-turn formed by residues Phe2 and Gly5 was observed in a 5 ns restrained molecular dynamics simulation using the implicit generalized Born solvent accessible surface area (GB/SA) solvation model. When subjected to 500 ps dynamics with explicit water both beta-turn folds were conserved throughout the simulations. The results obtained with implicit and explicit solvation models are compared, and their consistency with the nmr observations is discussed. The behavior of the linear pentapeptide in this study is in agreement with an earlier report on the consensus conformation of the insect kinin active core derived from analysis of cyclic active analogues.     

The curious case of Skokholm: equilibrium,non‐equilibrium and a phase shift in an island landbird assemblage

Previous work has indicated that the landbirds of Skokholm island (Wales) are not in equilibrium as defined in MacArthur–Wilson's classic theory of island biogeography. This study takes a new dataset with over six decades of data and investigates equilibrium on Skokholm using cluster analysis to identify periods of turnover stability. The attributes of the identified periods were investigated in relation to the MacArthur–Wilson model using analyses of change in numbers of species, S, from one year to the next and measures of variability in S quantified for each of the periods identified together with a consideration of the dynamics in the numbers of species by habitat groupings. Cluster analysis identified four main periods of which two middle periods appeared to be in equilibrium but with a phase shift in‐between. The first and last periods showed non‐equilibrium dynamics but plots of species by habitat groupings suggested that this was due to habitat changes going on at those times. This decadal long dataset indicates that the landbirds of Skokholm exhibit periods of both equilibrium and non‐equilibrium with the latter attributable to habitat change. The apparent phase shift in the equilibrium number of species was unexpected within the framework of island biogeographic theory and not easily explained using the current MacArthur–Wilson framework. There is a need to integrate the theory of island biogeography with more recent work on alternative stable states, tipping points, and phase (or regime) shifts, together with equilibrium and non‐equilibrium dynamics, into a single framework.     

关于《一类具时滞的神经网络模型的收敛性》的注记

本文研究了一类具有时滞的神经网络模型     

The structure and behavior of defoliating insect/forest systems

Using four detailed and complex simulation models we derive a framework for predicting behavior of any defoliating insect/forest system. The framework uses simple and easily gathered biological information on four sets of state variables, each with a characteristic temporal scale, to predict presence, absence or form of key ecological processes acting on or between the variables. The combination of these key processes enables prediction of system equilibrium structure and this structure can be used to derive the temporal behavior of the system. Four qualitatively different classes of system behavior arise from the equilibrium structures. The framework is tested against twelve other systems and field invalidation experiments are outlined. Forest defoliator research and management implications are discussed.     

密度分布非均匀的害虫和天敌生态模型的平衡解的稳定性

讨论一类密度分布非均匀的害虫和天敌生态模型平衡解的稳定性，得到该问题非负平衡解的存在性、渐适性和相应吸引区域。     

一类具年龄结构和接种的非终生免疫型传染病模型

研究一类具年龄结构和接种的非终生免疫SIRS传染病模型平衡解的稳定性.首先利用特征线法讨论了模型平衡解的存在性,然后利用比较定理和逐次迭代法得到无病平衡解与地方病平衡解全局稳定性的充分条件.     

Modeling Age-Specific Mortality for Countries with Generalized HIV Epidemics

Background

In a given population the age pattern of mortality is an important determinant of total number of deaths, age structure, and through effects on age structure, the number of births and thereby growth. Good mortality models exist for most populations except those experiencing generalized HIV epidemics and some developing country populations. The large number of deaths concentrated at very young and adult ages in HIV-affected populations produce a unique ‘humped’ age pattern of mortality that is not reproduced by any existing mortality models. Both burden of disease reporting and population projection methods require age-specific mortality rates to estimate numbers of deaths and produce plausible age structures. For countries with generalized HIV epidemics these estimates should take into account the future trajectory of HIV prevalence and its effects on age-specific mortality. In this paper we present a parsimonious model of age-specific mortality for countries with generalized HIV/AIDS epidemics.

Methods and Findings

The model represents a vector of age-specific mortality rates as the weighted sum of three independent age-varying components. We derive the age-varying components from a Singular Value Decomposition of the matrix of age-specific mortality rate schedules. The weights are modeled as a function of HIV prevalence and one of three possible sets of inputs: life expectancy at birth, a measure of child mortality, or child mortality with a measure of adult mortality. We calibrate the model with 320 five-year life tables for each sex from the World Population Prospects 2010 revision that come from the 40 countries of the world that have and are experiencing a generalized HIV epidemic. Cross validation shows that the model is able to outperform several existing model life table systems.

Conclusions

We present a flexible, parsimonious model of age-specific mortality for countries with generalized HIV epidemics. Combined with the outputs of existing epidemiological and demographic models, this model makes it possible to project future age-specific mortality profiles and number of deaths for countries with generalized HIV epidemics.     

再生数R0的计算及其控制策略

在传染病数学模型中,一般有一个传染病消除平衡点和至少一个地方病平衡点,这些平衡点的稳定性由再生数R_0决定,当R_0<1,疾病消除平衡点稳定,此传染病可以消除;当R_0>1,疾病消除平衡点不稳定,此传染病将蔓延,所以再生数R_0是传染病数学模型中最重要的参数.本文针对乙型肝炎病毒的传播方式以及各种状态间的转化模式建立了乙型肝炎数学模型,并利用马尔可夫链的方法计算乙型肝炎数学模型中的再生数R_0,提出了通过采取降低R_0的方法对乙型肝炎数学模型施加有效控制的策略.     

Heterozygosity in pin-thrum plants or with partial sex linkage

A two locus model is constructed for selection of a gene closely linked to the S locus in pin-thrum plants or to the sex determining part of the Y chromosome. Using this model, conditions for stability at the equilibrium point which is predicted by one-locus theory when there is heterozygotic superiority are derived. If the recombination value is small, it is found that this equilibrium point is unstable and that the gene frequencies go to a new stable equilibrium point at which the population has a higher average fitness. A few simple cases of selection and the implication of these to the theory of the evolution of the Y chromosome are discussed.     

一类含分布时滞的流行病模型的研究

提出了一类含分布时滞的流行病模型,利用构造李亚普诺夫泛函的方法,得到了无病平衡点和地方病平衡点全局稳定性的结论,揭示了平均时滞对各类平衡点稳定性的影响。     

From heroin epidemics to methamphetamine epidemics: Modelling substance abuse in a South African province

The global rise in the use of methamphetamine has been documented to have reached epidemic proportions. Researchers have focussed on the social implications of the epidemic. A typical drug use cycle consists of concealed drugs use after initiation, addiction, treatment-recovery-relapse cycle, whose dynamics are not well understood. The model by White and Comiskey [41], on heroin epidemics, treatment and ODE modelling, is modified to model the dynamics of methamphetamine use in a South African province. The analysis of the model is presented in terms of the methamphetamine epidemic threshold R₀. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable drug free equilibrium co-exists with a stable drug persistent equilibrium for a certain defined range of R₀. The stabilities of the model equilibria are ascertained and persistence conditions established. Furthermore, numerical simulations are performed; these include fitting the model to the available data on the number of patients with methamphetamine problems. The implications of the results to drug policy, treatment and prevention are discussed.