Global Properties of Infectious Disease Models with Nonlinear Incidence

We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number.     

Rattus exulans and the catastrophic disappearance of Hawai’i’s native lowland forest

Paleoenvironmental and archaeological investigations from the ’Ewa Plain of O’ahu provide insight into the problem of understanding lowland native forest loss in Hawai’i. Data from pollen analysis of a pond core record, avian paleontology, and archeology, document a precipitous decline of the native forest starting before Polynesian settlement on the ’Ewa Plain but after Polynesian colonization of O’ahu. It is hypothesized that rats, introduced by Polynesian colonizers, increased exponentially in the absence of significant predators or competitors, feeding on a largely endemic vegetation that had evolved in the absence of mammalian predators. Rats radiated ahead of human colonizers on O’ahu, eating their way through the vegetation, perhaps before the colonizers had encountered much of the pristine lowland forest into which the rats had radiated. This hypothesis is supported by several observations, including the almost complete absence of extinct or extirpated avian faunal remains in archaeological deposits, the present distribution of endemic vegetation in Hawai’i, rat ecology, population biology, and other evidence.

Population size and identity influence the reaction norm of the rare,endemic plant Cochlearia bavarica across a gradient of environmental stress

Habitat degradation and loss can result in population decline and genetic erosion, limiting the ability of organisms to cope with environmental change, whether this is through evolutionary genetic response (requiring genetic variation) or through phenotypic plasticity (i.e., the ability of a given genotype to express a variable phenotype across environments). Here we address the question whether plants from small populations are less plastic or more susceptible to environmental stress than plants from large populations. We collected seed families from small (<100) versus large natural populations (>1,000 flowering plants) of the rare, endemic plant Cochlearia bavarica (Brassicaceae). We exposed the seedlings to a range of environments, created by manipulating water supply and light intensity in a 2 x 2 factorial design in the greenhouse. We monitored plant growth and survival for 300 days. Significant effects of offspring environment on offspring characters demonstrated that there is phenotypic plasticity in the responses to environmental stress in this species. Significant effects of population size group, but mainly of population identity within the population size groups, and of maternal plant identity within populations indicated variation due to genetic (plus potentially maternal) variation for offspring traits. The environment x maternal plant identity interaction was rarely significant, providing little evidence for genetically- (plus potentially maternally-) based variation in plasticity within populations. However, significant environment x population-size-group and environment x population-identity interactions suggested that populations differed in the amount of plasticity, the mean amount being smaller in small populations than in large populations. Whereas on day 210 the differences between small and large populations were largest in the environment in which plants grew biggest (i.e., under benign conditions), on day 270 the difference was largest in stressful environments. These results show that population size and population identity can affect growth and survival differently across environmental stress gradients. Moreover, these effects can themselves be modified by time-dependent variation in the interaction between plants and their environment.     

Differential susceptibility epidemic models

We formulate compartmental differential susceptibility (DS) susceptible-infective-removed (SIR) models by dividing the susceptible population into multiple subgroups according to the susceptibility of individuals in each group. We analyze the impact of disease-induced mortality in the situations where the number of contacts per individual is either constant or proportional to the total population. We derive an explicit formula for the reproductive number of infection for each model by investigating the local stability of the infection-free equilibrium. We further prove that the infection-free equilibrium of each model is globally asymptotically stable by qualitative analysis of the dynamics of the model system and by utilizing an appropriately chosen Liapunov function. We show that if the reproductive number is greater than one, then there exists a unique endemic equilibrium for all of the DS models studied in this paper. We prove that the endemic equilibrium is locally asymptotically stable for the models with no disease-induced mortality and the models with contact numbers proportional to the total population. We also provide sufficient conditions for the stability of the endemic equilibrium for other situations. We briefly discuss applications of the DS models to optimal vaccine strategies and the connections between the DS models and predator-prey models with multiple prey populations or host-parasitic interaction models with multiple hosts are also given.This research was partially supported by the Department of Energy under contracts W-7405-ENG-36 and the Applied Mathematical Sciences Program KC-07-01-01.     

Entamoeba histolytica: the serine-rich gene polymorphism-based genetic variability of clinical isolates from Georgia

It is generally accepted that a majority of individuals infected by Entamoeba histolytica do not develop symptomatic disease. However, the parasite and the host factors contributing to the development of the disease, remain undetermined. It is also unclear why certain individuals develop extra-intestinal amebiasis without exhibiting apparent intestinal symptoms. An outbreak of amebic liver abscess in Tbilisi, Georgia in 1998-1999 suggested that the causative E. histolytica strain had an unusual propensity for extra-intestinal spread. To correlate the genetic differences with pathogenic potential of the parasite, we have examined the SREHP gene polymorphisms among Georgian E. histolytica isolates. Comparison of polymorphic patterns revealed the presence of several different genotypes of E. histolytica, thus preventing an association of a single genotype with hepatic disease, but supporting the previous finding of extensive genetic diversity among E. histolytica isolates from the same geographic origin.     

A Susceptible-infected Epidemic Model with Voluntary Vaccinations

An susceptible-infected epidemic model with endogenous behavioral changes is presented to analyze the impact of a prophylactic vaccine on disease prevalence. It is shown that, with voluntary vaccination, whether an endemic equilibrium exists or not does not depend on vaccine efficacy or the distribution of agent-types. Although an endemic equilibrium is unique in the absence of a vaccine, the availability of a vaccine can lead to multiple endemic equilibria that differ in disease prevalence and vaccine coverage. Depending on the distribution of agent-types, the introduction of a vaccine or, if one is available, a subsidy for vaccination can increase disease prevalence by inducing more risky behavior.I would like to thank one of the editors of the journal, Alan Hastings, for his comments and suggestions.     

硒对培养人胚肝细胞Ⅲ型前胶原,羟脯氨酸合成的影响

原代培养人胚肝细胞经１．１５６×１０￣(－７）ｍｏｌ／Ｌ硒预处理４ｈ,加入２０ｍｍｏｌ／Ｌ四氟化碳作用２０ｈ,观察硒对其Ⅲ型前胶原（ＰＣⅢ）和羟脯氨酸（Ｈｙｐ）生成的影响。结果培养液中ＰＣⅢ水平、细胞内Ｈｙｐ含量及细胞内外丙二醛（ＭＤＡ）水平均降低,与未加硒对照组比较差别有显著性（Ｐ＜０．０１）。而硒谷腕甘肽过氧化物酶（Ｓｅ－ＧＳＨ－ＰＸ）活性则较对照组显著增高（Ｐ＜０．００１）,且ＰＣⅢ水平与Ｓｅ－ＧＳＨ－Ｐ＿Ｘ／ＭＤＡ比值呈负相关（ｒ＝－０．９１５６,Ｐ＜０．０１）。提示硒可提高Ｓｅ－ＧＳＨ－Ｐ＿Ｘ／ＭＤＡ比值,抑制脂质过氧化激发的肝细胞胶原合成。     

High-elevation rock outcrop vegetation of the Southern Appalachian Mountains

Abstract. Species composition patterns and vegetation-environment relationships were quantified for high-elevation rock outcrops of the Southern Appalachian Mountains, an infrequent and insular habitat in a forested landscape. Outcrops occur over a wide geographic range encompassing extensive variation in both geology and climate. Geographic-scale factors interact with site-scale factors to produce variation in vegetation among outcrops. Similarly, site-scale factors interact with micro-scale factors to produce variation in vegetation within outcrops. To provide a quantitatively-based classification of outcrop vegetation we used a TWINSPAN analysis of 154 100-m² plots. We recognized nine communities that primarily correspond to different combinations of elevation, bedrock type, geography, and moisture. Within outcrops of a single bedrock type, vegetation composition of 100-m² plots was consistently correlated with elevation and solar radiation, but relationships to soil nutrients varied with bedrock type. Both site-scale (100 m²) factors (e.g. elevation, slope, aspect, and bedrock type) and plot-scale (1-m²) microsite factors (e.g. soil depth, vegetation height, soil nutrients) were strongly correlated with species composition at the 1-m² level. Environment can be used to predict composition more effectively for 100-m² plots on a single bedrock type than either across bedrock types or at a 1-m² scale. Composition-environment relationships resemble those described for outcrop systems from other regions with pronounced topographic relief more than they do those described for the nearby but flatter and lower-elevation outcrops of the Southeastern Piedmont. There is strong spatial autocorrelation in this community, perhaps owing to dispersal limitation. Consequently, a comprehensive conservation strategy must include reservation of both a range of geologic types and a range of geographic locations.     

永瓣藤濒危因素探讨

水瓣藤（MonimopetalumchinenseRehd．）是卫矛科（Celastraceae）的一个单种属植物,被列为国家二级珍稀濒危保护树种。永瓣藤濒危的因素主要是：（1）种子萌发障碍;（2）传粉受精不良,胚珠通常败育,结实率偏低;（3）种子成熟后胚因休眠或失水而失活;（4）人类活动对自然生态环境的严重干扰和破坏。本文提出了消除威胁生物多样性的社会因素、加强亚热带阔叶林生态系统的保护、重视自然保护区以外的就地保护工作、深入研究迁地保护的有效方法等保护策略。     

Integral equation models for endemic infectious diseases

Summary Endemic infectious diseases for which infection confers permanent immunity are described by a system of nonlinear Volterra integral equations of convolution type. These constant-parameter models include vital dynamics (births and deaths), immunization and distributed infectious period. The models are shown to be well posed, the threshold criteria are determined and the asymptotic behavior is analysed. It is concluded that distributed delays do not change the thresholds and the asymptotic behaviors of the models.This work was partially supported by NIH Grant AI 13233.