A mathematical model of avian influenza with half-saturated incidence

The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations. The effect of half-saturated incidence on transmission dynamics of the disease is investigated. The half-saturation constants determine the levels at which birds and humans contract avian influenza. To prevent the spread of avian influenza, the associated half-saturation constants must be increased, especially the half-saturation constant H _m for humans with mutant strain. The quantity H _m plays an essential role in determining the basic reproduction number of this model. Furthermore, by decreasing the rate β _m at which human-to-human mutant influenza is contracted, an outbreak can be controlled more effectively. To combat the outbreak, we propose both pharmaceutical (vaccination) and non-pharmaceutical (personal protection and isolation) control methods to reduce the transmission of avian influenza. Vaccination and personal protection will decrease β _m, while isolation will increase H _m. Numerical simulations demonstrate that all proposed control strategies will lead to disease eradication; however, if we only employ vaccination, it will require slightly longer to eradicate the disease than only applying non-pharmaceutical or a combination of pharmaceutical and non-pharmaceutical control methods. In conclusion, it is important to adopt a combination of control methods to fight an avian influenza outbreak.     

A discrete stage-structured two-species competition model with sexual and clonal reproduction

In this paper, we analyse a discrete stage-structured model which is a generalization of the two-species competition model studied in [2]. Motivated by plant populations, each species is assumed to reproduce both sexually and clonally. We show that this model has a dynamical behaviour that is similar to that of the classical continuous two-dimensional Lotka-Volterra model under weak nonlinearities of the Beverton-Holt type. By allowing the species to have different competition efficiencies, we show that it is possible to obtain different dynamics including coexistence, bistability and competitive exclusion, in contrast with the model studied in [2], which exhibits only competitive exclusion behaviour.     

甲型H1N1流感病毒在季流病毒、禽流感病毒共感染时变异可能性的验证

目的 甲型H1N1流感病毒A/California/7/2009分别与A/Brisbane/10/07和A/ShenZhen/406H/06共感染小型香猪,预测甲流病毒在与季流H3N2病毒/甲流病毒与禽流感病毒共感染时是否会发生变异.方法 分别将A/California/7/2009(CA7)与A/Brisbane/10/07(H3N2),A/California/7/2009与A/Shenzhen/406H/06(H5N1)对5～6月龄小型猪共感染,小型猪经复方氯胺酮0.1 mL/kg麻醉后进行滴鼻感染,感染后第5天安乐死动物,取动物肺组织作病毒测序分析.结果 A/California/7/2009(CA7)与A/Brisbane/10/07(H3N2)共感染后,A/California/7/2009病毒PB1基因993位G→A突变,PA基因1659位G→A突变,没有氨基酸的变异.A/California/7/2009与A/Shenzhen/406H/06(H5N1)共感染后A/California/7/2009病毒PB2基因1711位T→C突变.碱基的突变未引起氨基酸的变异.结论 A/California/7/2009(CA7)与A/Brisbane/10/07(H3N2),A/California/7/2009与A/Shenzhen/406H/06(H5N1)共感染后在猪的体内没有发生病毒重组、变异.     

A three-stage discrete-time population model: continuous versus seasonal reproduction

We consider a three-stage discrete-time population model with density-dependent survivorship and time-dependent reproduction. We provide stability analysis for two types of birth mechanisms: continuous and seasonal. We show that when birth is continuous there exists a unique globally stable interior equilibrium provided that the inherent net reproductive number is greater than unity. If it is less than unity, then extinction is the population's fate. We then analyze the case when birth is a function of period two and show that the unique two-cycle is globally attracting when the inherent net reproductive number is greater than unity, while if it is less than unity the population goes to extinction. The two birth types are then compared. It is shown that for low birth rates the adult average number over a one-year period is always higher when reproduction is continuous. Numerical simulations suggest that this remains true for high birth rates. Thus periodic birth rates of period two are deleterious for the three-stage population model. This is different from the results obtained for a two-stage model discussed by Ackleh and Jang (J. Diff. Equ. Appl., 13, 261-274, 2007), where it was shown that for low birth rates seasonal breeding results in higher adult averages.     

The impact of seasonal and year-round transmission regimes on the evolution of influenza A virus

Punctuated antigenic change is believed to be a key element in the evolution of influenza A; clusters of antigenically similar strains predominate worldwide for several years until an antigenically distant mutant emerges and instigates a selective sweep. It is thought that a region of East-Southeast Asia with year-round transmission acts as a source of antigenic diversity for influenza A and seasonal epidemics in temperate regions make little contribution to antigenic evolution. We use a mathematical model to examine how different transmission regimes affect the evolutionary dynamics of influenza over the lifespan of an antigenic cluster. Our model indicates that, in non-seasonal regions, mutants that cause significant outbreaks appear before the peak of the wild-type epidemic. A relatively large proportion of these mutants spread globally. In seasonal regions, mutants that cause significant local outbreaks appear each year before the seasonal peak of the wild-type epidemic, but only a small proportion spread globally. The potential for global spread is strongly influenced by the intensity of non-seasonal circulation and coupling between non-seasonal and seasonal regions. Results are similar if mutations are neutral, or confer a weak to moderate antigenic advantage. However, there is a threshold antigenic advantage, depending on the non-seasonal transmission intensity, beyond which mutants can escape herd immunity in the non-seasonal region and there is a global explosion in diversity. We conclude that non-seasonal transmission regions are fundamental to the generation and maintenance of influenza diversity owing to their epidemiology. More extensive sampling of viral diversity in such regions could facilitate earlier identification of antigenically novel strains and extend the critical window for vaccine development.     

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.     

禽流感与禽流感病毒研究进展

对禽流感的症状、传播、感染、流行规律、疾病发生历史、流行监测、诊断、防治以及禽流感病毒的分类地位、命名、病毒粒子形态结构、病毒基因组结构、病毒复制、病毒变异的研究进展作了综合评述,并对该领域的研究热点和方向作了探讨。     

Shortcomings of vitamin D-based model simulations of seasonal influenza

Seasonal variation in serum concentration of the vitamin D metabolite 25(OH) vitamin D [25(OH)D], which contributes to host immune function, has been hypothesized to be the underlying source of observed influenza seasonality in temperate regions. The objective of this study was to determine whether observed 25(OH)D levels could be used to simulate observed influenza infection rates. Data of mean and variance in 25(OH)D serum levels by month were obtained from the Health Professionals Follow-up Study and used to parameterize an individual-based model of influenza transmission dynamics in two regions of the United States. Simulations were compared with observed daily influenza excess mortality data. Best-fitting simulations could reproduce the observed seasonal cycle of influenza; however, these best-fit simulations were shown to be highly sensitive to stochastic processes within the model and were unable consistently to reproduce observed seasonal patterns. In this respect the simulations with the vitamin D forced model were inferior to similar modeling efforts using absolute humidity and the school calendar as seasonal forcing variables. These model results indicate it is unlikely that seasonal variations in vitamin D levels principally determine the seasonality of influenza in temperate regions.     

A simple stochastic model with environmental transmission explains multi-year periodicity in outbreaks of avian flu

Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2-8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission.     

Immunity to seasonal and pandemic influenza A viruses

The introduction of a new influenza strain into human circulation leads to rapid global spread. This review summarizes innate and adaptive immunity to influenza viruses, with an emphasis on T-cell responses that provide cross-protection between distinct subtypes and strains. We discuss antigenic variation within T-cell immunogenic peptides and our understanding of pre-existing immunity towards the pandemic A(H1N1) 2009 strain.     

Stability in an insect-pathogen model incorporating age-dependent immunity and seasonal host reproduction

A modified SIRS model is developed as a framework for the study of epizootiological dynamics in an insect-pathogen system. Linearized stability analysis reveals that the system with one immune and one susceptible host class can exhibit stable, periodic or unstable behavior depending on model parameters. In general, high pathogenicity, short pathogen propagule lifespan and high host reproductive rate are stabilizing influences. Pathogen transmissibility and propagule production/host do not influence local stability. The effect of seasonal host reproduction is studied because most insect hosts are seasonal in temperate climates. The basic stability dependence on model parameters holds except as modified by the length of the reproduction interval. The results of this study are compared with the recent work of Anderson and May. Scientific paper No. 82-7-179 of the Kentucky Agricultural Experiment Station, Lexington. This research has been financed in part with Federal funds from the USDA under grant number 82-CRSR-2-1000. The contents do not necessarily reflect the views and policies of the USDA.     

Enzymological characteristics of avian influenza A virus neuraminidase

Neuraminidases of 18 strains of avian influenza A virus were examined by both colorimetric and fluorometric assays using fetuin and 4-methylumbelliferyl-N-Ac-alpha-D-neuraminide as substrates, respectively, to compare them with those of human influenza A and B viruses. The ratios of the neuraminidase activity of avian influenza virus measured by the colorimetric assay method to that measured by the fluorometric assay were distributed in the range of 2.4-20.3. The enzyme of avian influenza virus showed calcium-ion dependence in both assay methods. These results suggest that neuraminidase of avian influenza A virus is varies greatly from one strain to another in substrate specificity as compared with those of human influenza A and B viruses, and that some strains of avian influenza A virus have a neuraminidase with unique enzymological characteristics different from that of human influenza A virus as well as that of influenza B virus.     

Regulation of seasonal reproduction in mollusks

Understanding the physiological basis of environmental regulation of reproduction at the cellular level has been difficult or unfeasible in vertebrate species because of the highly complex and diffuse nature of vertebrate neuroendocrine systems. This is not the case with the simple nervous system of mollusks in which reproductive neuroendocrine cells are often readily identifiable in living tissue. Given that there are mollusks that are seasonal breeders, that the neuroendocrine cells controlling reproduction have been identified in several molluskan species, that these neurons are conducive to cell physiological analysis, and that basic features of cell biology have been highly conserved between mammals and mollusks, it seems that the mollusk would provide an excellent model system to investigate cell-physiological events that mediate effects of environmental signals on reproduction. The purpose of this review is to explore this idea in three species in which the topic of the neural basis of seasonal reproduction has been studied: the giant garden slug Limax maximus, the freshwater pond snail Lymnaea stagnalis, and the marine snail Aplysia californica.     

H7N9禽流感病毒小鼠感染动物模型的建立

目的建立H7N9禽流感病毒小鼠感染模型。方法 1×108,1×107或1×106TCID50H7N9禽流感病毒原液(A/Anhui/1/2013)滴鼻感染BALB/c小鼠。主要观测指标:临床症状、死亡率、病理变化、病毒载量和血清抗体检测。结果被感染的小鼠表现为竖毛、弓背、体重下降;病理表现为间质性肺炎,感染后第2天开始在呼吸道脱落细胞中检测到病毒;免疫组化或病毒分离方法在肺、肾、脑、肠、脾等组织检测到病毒;感染后14 d在小鼠血清中血凝抑制试验特异性抗体效价达到160;淋巴细胞减少,中性粒细胞增多。结论 H7N9感染BALB/c小鼠模型与人类禽流感感染疾病的基本特征相似,为研究该病的发病机制及药物疫苗的研发提供了工作基础。     

The seasonal timing of reproduction:

Summary Dissection of 1,941 specimens provided data on reproductive cycles in six genera of skinks and three genera of agamids from the Alligator Rivers Region of Australia's Northern Territory. Comparative data on lizards from the temperate zone were gathered by dissecting specimens of three genera, and by reviewing published studies. The Alligator Rivers Region climate exhibits uniformly high temperatures but extremely seasonal rainfall. By analogy with studies on tropical herpetofaunas in other parts of the world, we hypothesised that most species would breed during the wet-season.Instead, a great diversity in the seasonal timing of reproduction in tropical lizards was observed. For example, among the skinks,Cryptoblepharus breeds year-round,Carlia andSphenomorphus breed in the wet-season, whereasLerista, Morethia and most (but not all)Ctenotus breed during the dry-season. Among the agamids,Diporiphora andGemmatophora breed in the wet-season, andChelosania in the dry-season. Temperate-zone lizards in Australia show less interspecific variation: all species breed in late spring and summer.Hypotheses concerning the evolutionary determinants of reproductive seasonality are reviewed in the light of these data. Thermal tolerances of developing embryos are unlikely to be important in determining breeding seasons of the Alligator Rivers Region herpetofauna, as there is little seasonal variation in temperature. Differences in reproductive timing between microsympatric species are inconsistent with hypotheses giving a major role to the seasonality of fire, flooding or intensity of predation. There is no clear association between food habits and reproductive timing. The best predictor of breeding seasonality seems to be the biogeographic history of the taxon. Alligator Rivers Region representatives of arid-zone taxa tend to breed in the dryseason, whereas representatives of mesic-adapted lineages tend to be wet-season breeders. A species from one cosmopolitan genus breeds year-round. We hypothesize that embryonic moisture tolerances may be an important determinant of breeding seasonality in this region, although some cases do not support this conclusion.