The Predictive Power of R 0 in an Epidemic Probabilistic System

An important issue in theoretical epidemiology is the epidemic thresholdphenomenon, which specify the conditions for an epidemic to grow or die out.In standard (mean-field-like) compartmental models the concept of the basic reproductive number, R ₀, has been systematically employed as apredictor for epidemic spread and as an analytical tool to study thethreshold conditions. Despite the importance of this quantity, there are nogeneral formulation of R ₀ when one considers the spread of a disease ina generic finite population, involving, for instance, arbitrary topology ofinter-individual interactions and heterogeneous mixing of susceptible andimmune individuals. The goal of this work is to study this concept in ageneralized stochastic system described in terms of global and localvariables. In particular, the dependence of R ₀ on the space ofparameters that define the model is investigated; it is found that near ofthe `classical' epidemic threshold transition the uncertainty about thestrength of the epidemic process still is significantly large. Theforecasting attributes of R ₀ for a discrete finite system is discussedand generalized; in particular, it is shown that, for a discrete finitesystem, the pretentious predictive power of R ₀ is significantlyreduced.     

Dynamics of Mycoplasmal Conjunctivitis in the Native and Introduced Range of the Host

In 1994, Mycoplasma gallisepticum, a common bacterial poultry pathogen, caused an epidemic in house finches in the eastern part of their North American range where the species had been introduced in the 1940s. Birds with mycoplasmal conjunctivitis were reported across the entire eastern United States within 3–4 years. Here we track the course of the Mycoplasma gallisepticum epidemic as it reached native, western North American populations of the house finch. In 2002, Mycoplasma gallisepticum was first observed in a native house finch population in Missoula, MT, where it gradually increased in prevalence during the next 2 years. Concurrently, house finches with conjunctivitis were reported with increasing number in the Pacific Northwest. In native populations of the host, the epidemic expanded more slowly, and reached lower levels of prevalence than in the eastern, introduced range of the species. Maximal prevalence was about half in the Missoula population than in local populations in the East. Although many factors can contribute to these differences, we argue that it is most likely the higher genetic heterogeneity in western than in eastern populations caused the lower impact of the pathogen.     

The Potential Impact of Disease on the Migratory Structure of a Partially Migratory Passerine Population

Since its introduction into eastern North America in the 1940s, the eastern population of house finches (Carpodacus mexicanus) has become partially migratory, unlike its nonmigratory source population in southern California (Able and Belthoff in Proc. R. Soc. Lond. 265 (1410), 2063–2071, 1998; Belthoff and Gauthreaux in Condor 93, 374–382, 1991). The infectious disease mycoplasmal conjunctivitis (pathogen Mycoplasma gallisepticum or “MG”), which has been monitored in the house finch population since its appearance around 1993 (Dhondt et al. in J. Wild. Dis. 34 (2), 265–280, 1998), may induce higher mortality rates among populations in more northerly latitudes relative to more southerly populations. Here, we investigate the potential impact of this differential disease mortality on the migratory structure of the eastern house finch population using an epidemic modeling approach. Analytical and computational results suggest the ongoing MG epidemic in the eastern house finch could lead to increases in the percentage of and the total number of migrating individuals in a population despite overall population declines, assuming relatively high winter mortality rates in the north eastern part of their range. These results also suggest that empirical evidence of such a change in migratory structure would be most noticeable in northerly inland populations that showed significant declines following the initial outbreak of MG in the east.     

An SEI model for sarcoptic mange among chamois

We consider a simple model to study the dynamics of sarcoptic mange in a population of chamois. The epidemiological patterns observed during an epidemic in Italy are reconstructed and key parameters of the model are estimated from field data. In particular, we calculate the basic reproductive ratio R ₀, a threshold value for chamois density for the occurrence of an epidemic and the speed of propagation of the epidemic wave. The model is then used to obtain indications on the effect of culling as a possible control measure in a closed population and extended to analyse the spatial diffusion of the epidemic. Our results are in agreement with mange epidemiology and observations, and suggest that intervention could be efficacious in reducing the impact of an epidemic.     

三峡库区松材线虫病扩张速度对人为活动的响应

松材线虫病是我国森林重要的检疫性病害,除自然媒介天牛传播,人为因素介导的传播在松材线虫病扩散和蔓延中起着至关重要的作用。选择在我国松材线虫病的重点发生区域三峡库区,研究马尾松林景观格局和以人为活动强度为主要因子的松材线虫病扩散规律,尝试揭示松材线虫病扩散机制。结果显示三峡库区的疫点数在近年有上升趋势,各地区发病率得到一定控制;在疫区和非疫区,马尾松林斑块聚合度最大的是非疫区的大渡口,为98.6406;斑块分离度最大的是非疫区的秭归,为0.9318;方差分析结果显示马尾松林景观格局和松材线虫病之间没有相关性。进一步研究了松材线虫病和人为活动强度的联系,结果显示松材线虫病发病率和地区路网密度、人口总量具有较强的相关性,和地区GDP、货运周转量相关性小。宜昌的松材线虫病发病率和路网密度的相关系数为0.985,和人口总数的相关系数为0.866;重庆的松材线虫病发病率和路网密度相关系数为0.924,和人口总数相关系数为0.999;其次基于路网密度和人口总数,对三峡库区松材线虫病疫情在未来十年进行了预测,结果显示随着路网密度和人口总数的扩增,宜昌松材线虫病也将呈现逐步增大的趋势,R~2值为0.919和0.637;重庆发生趋势一致,R~2值为0.976和0.992。     

The system management approach of biological weed control: Some theoretical considerations and aspects of application

Theoretical considerations behind the system management approach of biological weed control are presented. These include, a part describing and explaining the effects of parasitic fungi on crop – weed competition, a part describing and explaining the epidemic spread of parasitic fungi on weeds, and a part relating crop – weed competition at the population level to epidemics. The theoretical framework developed may also provide a basis for the use of other natural enemies, like insects, for biological weed control following the system management approach. Aspects of application are discussed using data of the interaction between the annual weed Senecio vulgaris and the rust fungusPuccinia lagenophorae.     

A general model for stochastic SIR epidemics with two levels of mixing

This paper is concerned with a general stochastic model for susceptible→infective→removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution ‘centred’ on that infective, and each global contact is with an individual chosen independently and uniformly from the whole population. The asymptotic situation in which the local contact distribution remains fixed as the population becomes large is considered. The concepts of local infectious clump and local susceptibility set are used to develop a unified approach to the threshold behaviour of this class of epidemic models. In particular, a threshold parameter R_* governing whether or not global epidemics can occur, the probability that a global epidemic occurs and the mean proportion of initial susceptibles ultimately infected by a global epidemic are all determined. The theory is specialised to (i) the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective’s household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts are nearest-neighbour.     

Epidemiology of a <Emphasis Type="Italic">Daphnia</Emphasis> brood parasite and its implications on host life-history traits

Parasites influence host life-history traits and therefore might crucially shape host populations in natural systems. In a series of laboratory experiments, we studied the impact of an oomycete brood parasite on its Daphnia (waterflea) host. We asked whether Daphnia dump the infected brood and subsequently are able to reproduce again as was occasionally observed in a preliminary study. No viable offspring developed from infected clutches, but 78% of the infected females produced healthy offspring after releasing the infected brood while molting. Neither those offsprings’ development success nor their mothers’ reproductive potential was affected by the brood parasite. However, infected Daphnia had a reduced life-span and suffered an increased susceptibility to another parasite, an unidentified bacterium. Additionally, we studied the prevalence of this brood parasite and the unidentified bacterium in a natural Daphnia assemblage in a pre-alpine lake, across changing demographic and environmental conditions. The brood parasite epidemic seemed to be host-density dependent. Our results show that the brood parasite’s impact on the host population is enhanced when combined with the unidentified bacterium.     

Seasonal dynamics and thresholds governing recurrent epidemics

Driven by seasonality, many common recurrent infectious diseases are characterized by strong annual, biennial and sometimes irregular oscillations in the absence of vaccination programs. Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S ₀ of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S ₀ are more reliable than those based on the classical reproductive number R ₀ from the conventional theory.      

Epidemiology of anther-smut disease (Microbotryum violaceum) and numeric regulation of populations ofSilene dioica

Summary The interaction between the anther smutMicrobotryum violaceum and its hostSilene dioica was studied during 1985–1990 in 47 populations of different ages, sizes and densities, in an archipelago area in northern Sweden. The sizes of these populations had also been surveyed in the early 1970s. Our results indicate that establishment ofMicrobotryum violaceum is host-size and density dependent. Firstly, young populations ofSilene dioica that became diseased during the study were larger and tended to be more dense than young populations that remained healthy. Secondly, populations diseased in both 1985 and 1990 were found to be larger and tended to be more dense than populations healthy in both years. We were able to document that the pathogen actually failed to establish in two small young populations (diseased plants died shortly after they appeared) and did go extinct in one small old population. Disease incidences within populations did not show large fluctuations between years. The highest increases in disease incidence during the study were found in three relatively young populations that were disease-free at the start of the study. Older populations highly diseased at the start showed less of an increase. Our study indicates thatMicrobotryum violaceum acts as a regulatory factor influencing the rate of increase inSilene dioica populations, once they are sufficiently large to maintain the pathogen. Firstly, seedling density decreased with increased incidence of disease and a seed addition experiment indicated seed-limited recuritment in highly diseased populations. Secondly, those populations that reached very large sizes or densities were either healthy or had very low incidences, indicating the potential for populations that for one reason or another escape an epidemic. However, in the comparison of changes in population size over 16–18 years there was no simple correlation between expansion rate and disease incidence.     

Genetic diversity of rhizobia associated with <Emphasis Type="Italic">Vicia faba</Emphasis> in three ecological regions of China

Great genetic diversity was revealed among 75 rhizobal isolates associated with Vicia faba grown in Chinese fields with AFLP, ARDRA, 16S rDNA sequencing, DNA–DNA hybridization, BOX-PCR and RFLP of PCR-amplified nodD and nodC. Most of the isolates were Rhizobium leguminosarum, and six isolates belonged to an unnamed Rhizobium species. In the homogeneity analysis, the isolates were grouped into three clusters corresponding to (1) autumn sowing (subtropical) region where the winter ecotype of V. faba was cultivated, (2) spring sowing (temperate) region where the spring ecotype was grown, and (3) Yunnan province where the intermediate ecotype was sown either in spring or in autumn. Nonrandom associations were found among the nod genotypes, genomic types and ecological regions, indicating an epidemic symbiotic gene transfer pattern among different genomic backgrounds within an ecological region and a relatively limited transfer pattern between different regions. Conclusively, the present results suggested an endemic population structure of V. faba rhizobia in Chinese fields and demonstrated a novel rhizobium associated with faba bean. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A discrete branching process model for the spread of HIV via steady sexual partnerships

The transmission of HIV in a monogamous heterosexual population structured by the ordinal number of the current partnership is considered. The sexual carreer of a man (woman) is thought to be a succession of k(m) partnerships, and a multitype Galton-Watson process is defined, in which the objects are infections and the types are related to the ordinal number of the partnership during which a person has acquired the infection. Contrary to multitype models in which the types are not age-related in some sense, this process contains at least two singular types, namely infections acquired in the last partnership of a man or a woman. The criticality parameter of this branching process is the epidemic threshold parameter R₀. In the case k=m an epidemic is impossible, however large k may be, if the difference between the ordinal numbers of the partners in a pair is never > 1. When the frequency of pairs in which this difference is 2 increases, then R₀ increases. This is demonstrated for the cases k=m=3 and k=4,m=3. The formulae obtained show also the joint influence of the mixing pattern and of variable infectivity. The result for the case of uniform mixing implies that a formula of May and Anderson (1987) is an approximation for k and m large.Mathematics Subject Classification (2000): 92D (primary), 60J (secondary)     

Approximation of the Basic Reproduction Number <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> for Vector-Borne Diseases with a Periodic Vector Population

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R ₀ of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p ₀ (1+ε cos (ωt − φ)) with ε ≪ 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p ₀. The maximum correction due to the second term is (ε²/8)% and always tends to decrease R ₀. The basic reproduction number R ₀ is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R ₀ are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality. MSC 92D30 ⋅ 45C05 ⋅ 47A55     

Abortive embryogenesis in hybrid swarm populations of <Emphasis Type="Italic">Pinus sylvestris</Emphasis> L. and <Emphasis Type="Italic">Pinus muga</Emphasis> Turra

Comparative study on fertilization process in Pinus sylvestris, Pinus mugo and in their putative hybrid swarm individuals was done involving pre-zygotic and post-zygotic stages. The amount of surviving ovules from open pollination reflecting the mode of interaction between pollen grains and nucellar tissue of an ovule averaged at 8.1 of sound ovules per conelet in Pinus sylvestris, 7.3 ovules in the hybrid swarm population and at 4.9 ovules in Pinus mugo. A strong correlation was observed between the number of surviving ovules and the proportion of germinating seeds in the compared species and hybrids. Normal course of embryogenesis in Pinus sylvestris and Pinus mugo contrasted with increased frequency of disturbances observed in the hybrid swarm individuals. The differential survival rates of the ovules and deviations from typical pattern of embryogenesis are discussed from the standpoint of cross-ability relationship between Pinus sylvestris and Pinus mugo.     

Differences in above- and below-ground responses to ozone between two populations of a perennial grass

Our study examined the influence of elevated ozone levels on the growth and mycorrhizal colonization of two populations of Elymus glaucus L. (blue wildrye). We hypothesized that ozone would reduce carbon availability to the plants, particularly below ground, and would affect mycorrhizal colonization. Because of the wide geographic range of E. glaucus, two populations of plants were selected from areas of contrasting ozone histories to examine intraspecies variation in response to ozone. Two populations of E. glaucus (southern California versus northern California) exposed in a factorial experiment involving ozone, mycorrhizal inoculation with Glomus intraradices Schenck and Smith, and plant source population. Ozone had a subtle effect on leaf area and number of tillers but did not affect overall root:shoot ratio in either population. The impact of ozone on above-ground growth characteristics was most pronounced in the southern population that came from a high-ozone environment, while below-ground responses such as reduced arbuscular colonization was most pronounced in the northern population which originated in a low-ozone environment. Further analysis of soil characteristics from the northern population of plants revealed a significant reduction in active soil bacterial biomass and an increase in total fungi per gram dry weight soil, suggesting a possible role for ozone in altering soil processes. Whether or not population differences in response to ozone were due to genetic shifts resulting from prior ozone remains to be determined. However, these subtle but important differences in population response to ozone above- and below-ground have significant implications in any attempt to generalize plant response, even within a species. Future research efforts need to include better characterization of intraspecific variation in response to ozone as well as possible adaptive strategies that may result from chronic ozone exposure.     

Threshold Conditions for a Non-Autonomous Epidemic System Describing the Population Dynamics of Dengue

A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by , is less than 1, the disease does not invade the populations and when is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases. An erratum to this article can be found at     

Stemming the obesity epidemic: a tantalizing prospect

Objective: Obesity is a growing problem worldwide, but there are no good methods to assess the future course of the epidemic and the potential influence of interventions. We explore the behavior change needed to stop the obesity epidemic in the U.S. Research Methods and Procedures: We modeled the population distribution of BMI as a log‐normal curve of which the mean shifts upward with time due to a positive population energy balance. Interventions that decrease food intake or increase physical activity result in more favorable trends in BMI. Results: The recently observed trend in average BMI implies that the average U.S. adult over‐consumes by ～10 kcal/d. If this trend continues unaltered, obesity prevalence will exceed 40% for men and 45% for women in 2015. To stop the epidemic, it suffices to decrease caloric consumption by ～10 kcal or walk an extra 2 to 3 minutes per day, on average. Discussion: This leads to a paradox: little behavior change seems sufficient to halt the epidemic, but in practice this proves hard to achieve. The obesogenic environment is the likely culprit. Individuals trying to maintain a healthy weight need to be supported by environments that stimulate physical activity and do not encourage over‐consumption. Research should show what measures are effective.     

Breeding system and crossability in JapaneseEpimedium (Berberidaceae)

A series of experimental pollinations involving six species ofEpimedium provided strong evidence for an outbreeding system and no internal (postmating, postpollination) barrier to hybridization in the taxa concerned. Self-pollinations of four species,E. diphyllum, E. trifoliatobinatum, E. grandiflorum andE. sempervirens indicated high self-incompatibility (at most 5.4%, usually 0% in capsule-set). Field experiments in a population revealed the occurrence of cross-pollination. On the other hand, interspecific cross-pollinations showed high crossability at any combination of species (33.3%–100% in capsule-set). Furthermore, the interspecific F₁s obtained germinated at a high rate (usually more than 20%) and three of them, which bloomed, are highly fertile (more than 68.6% in pollen viability). The results were discussed in connection with the isolating mechanisms between the species ofEpimedium.     

The spatial spread and final size of models for the deterministic host-vector epidemic

A disease is considered which is transferred between two populations, termed hosts and vectors. The disease is transmitted solely from infected vector to uninfected host and from infected host to uninfected vector. Two models are formulated in which infectious individuals are introduced at time t = 0 into the populations of susceptibles, thus triggering an epidemic through those populations. Conditions are established for a major epidemic to occur, and the final size of the epidemic is obtained for these models when no spatial aspect is considered. When a spatial aspect is included in the models, again the condition for a major epidemic is obtained. The pandemic theorem is proved rigorously, giving a lower bound for the proportion of each population, at each point, who eventually suffer the epidemic. The behavior a long way from the initial focus of infection is also rigorously obtained.     

Drug Addiction - Pushers Generated from the Addicts

This work develops a model for the spread of drug addiction in a closed population of size N. The spread of addiction is considered as an epidemic process where the addicts mix homogeneously within the population. There is an additional group (or pushers) with whom the susceptibles interact, but who are generated from the addicts. State probabilities and moments are obtained for this stochastic process. An extension to a generalized model is also made.