A Contact-Network-Based Formulation of a Preferential Mixing Model

Heterogeneity in the number of potentially infectious contacts and connectivity correlations (“like attaches to like” i.e., assortatively mixed or “opposites attract” i.e., disassortatively mixed) have important implications for the value of the basic reproduction ratio R ₀ and final epidemic size. In this paper, we present a contact-network-based derivation of a simple differential equation model that accounts for preferential mixing based on the number of contacts. We show that results based on this model are in good qualitative agreement with results obtained from preferential mixing models used in the context of sexually transmitted diseases (STDs). This simple model can accommodate any mixing pattern ranging from completely disassortative to completely assortative and allows the derivation of a series of analytical results.     

The asymptotic final size distribution of reducible multitype Reed-Frost processes

The asymptotic final size distribution of a multitype Reed-Frost process, a chain-binomial model for the spread of infection in a finite, closed multitype population, is derived in the case of reducible contact pattern between types. The results are obtained using techniques developed for the irreducible case.     

Stochastic model of an influenza epidemic with drug resistance

A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R(0), is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.     

The effect of contact heterogeneity and multiple routes of transmission on final epidemic size

Heterogeneity in the number of potentially infectious contacts amongst members of a population increases the basic reproduction ratio (R(0)) and markedly alters disease dynamics compared to traditional mean-field models. Most models describing transmission on contact networks only account for one specific route of transmission. However, for many infectious diseases multiple routes of transmission exist. The model presented here captures transmission through a well defined network of contacts, complemented by mean-field type transmission amongst the nodes of the network that accounts for alternative routes of transmission. The impact of these combined transmission mechanisms on the final epidemic size is investigated analytically. The analytic predictions for the purely mean-field case and the transmission through the network-only case are confirmed by individual-based network simulations. There is a critical transmission potential above which an increased contribution of the mean-field type transmission increases the final epidemic size while an increased contribution of the transmission through the network decreases it. Below the critical transmission potential the opposite effect is observed.     

Rural–urban gradient in seasonal forcing of measles transmission in Niger

Seasonally driven cycles of incidence have been consistently observed for a range of directly transmitted pathogens. Though frequently observed, the mechanism of seasonality for directly transmitted human pathogens is rarely well understood. Despite significant annual variation in magnitude, measles outbreaks in Niger consistently begin in the dry season and decline at the onset of the seasonal rains. We estimate the seasonal fluctuation in measles transmission rates for the 38 districts and urban centres of Niger, from 11 years of weekly incidence reports. We show that transmission rates are consistently in anti-phase to the rainfall patterns across the country. The strength of the seasonal forcing of transmission is not correlated with the latitudinal rainfall gradient, as would be expected if transmission rates were determined purely by environmental conditions. Rather, seasonal forcing is correlated with the population size, with larger seasonal fluctuation in more populous, urban areas. This pattern is consistent with seasonal variation in human density and contact rates due to agricultural cycles. The stronger seasonality in large cities drives deep inter-epidemic troughs and results in frequent local extinction of measles, which contrasts starkly to the conventional observation that large cities, by virtue of their size, act as reservoirs of measles.     

An epidemic model with infector and exposure dependent severity

A stochastic epidemic model allowing for both mildly and severely infectious individuals is defined, where an individual can become severely infectious directly upon infection or if additionally exposed to infection. It is shown that, assuming a large community, the initial phase of the epidemic may be approximated by a suitable branching process and that the main part of an epidemic that becomes established admits a law of large numbers and a central limit theorem, leading to a normal approximation for the final outcome of such an epidemic. Effects of vaccination prior to an outbreak are studied and the critical vaccination coverage, above which only small outbreaks can occur, is derived. The results are illustrated by simulations that demonstrate that the branching process and normal approximations work well for finite communities, and by numerical examples showing that the final outcome may be close to discontinuous in certain model parameters and that the fraction mildly infected may actually increase as an effect of vaccination.     

Solar radiation decreases parasitism in Daphnia

Climate change and variation in atmospheric ozone are influencing the intensity of ultraviolet radiation (UVR) reaching ecosystems. Changing UVR regimes, in turn, may alter epidemics of infectious disease. This possibility hinges on the sensitivity of epidemiologically relevant traits of host and parasite to UVR. We address this issue using a planktonic system (a zooplankton host, Daphnia dentifera, and its virulent fungal parasite, Metschnikowia bicuspidata). Controlled laboratory experiments, coupled with in situ field incubations of spores, revealed that quite low levels of UVR (as well as longer wavelength light) sharply reduced the infectivity of fungal spores but did not affect host susceptibility to infection. The parasite's sensitivity to solar radiation may underlie patterns in a lake survey: higher penetration of solar radiation into lakes correlated with smaller epidemics that started later in autumn (as incident sunlight declined). Thus, solar radiation, by diminishing infectivity of the parasite, may potently reduce disease.     

Effect of Predators of Juvenile Rodents on the Spread of the Hantavirus Epidemic

Effects of predators of juvenile mice on the spread of the Hantavirus are analyzed in the context of a recently proposed model. Two critical values of the predation probability are identified. When the smaller of them is exceeded, the hantavirus infection vanishes without extinguishing the mice population. When the larger is exceeded, the entire mice population vanishes. These results suggest the possibility of control of the spread of the epidemic by introducing predators in areas of mice colonies in a suitable way so that such control does not kill all the mice but lowers the epidemic spread.     

Costs and benefits of group living with disease: a case study of pneumonia in bighorn lambs (Ovis canadensis)

Group living facilitates pathogen transmission among social hosts, yet temporally stable host social organizations can actually limit transmission of some pathogens. When there are few between-subpopulation contacts for the duration of a disease event, transmission becomes localized to subpopulations. The number of per capita infectious contacts approaches the subpopulation size as pathogen infectiousness increases. Here, we illustrate that this is the case during epidemics of highly infectious pneumonia in bighorn lambs (Ovis canadensis). We classified individually marked bighorn ewes into disjoint seasonal subpopulations, and decomposed the variance in lamb survival to weaning into components associated with individual ewes, subpopulations, populations and years. During epidemics, lamb survival varied substantially more between ewe-subpopulations than across populations or years, suggesting localized pathogen transmission. This pattern of lamb survival was not observed during years when disease was absent. Additionally, group sizes in ewe-subpopulations were independent of population size, but the number of ewe-subpopulations increased with population size. Consequently, although one might reasonably assume that force of infection for this highly communicable disease scales with population size, in fact, host social behaviour modulates transmission such that disease is frequency-dependent within populations, and some groups remain protected during epidemic events.     

Simple Epidemic Models with Positive Latent Period

This paper deals with two types of simple epidemic models, namely, deterministic and stochastic wherein the latent period is assumed to be positive. In the deterministic epidemic model, the distributions of susceptibles, inactive infectives, active infectives and that of epidemic curve which gives the rate at which new infections take place have been obtained. The expression for the expected time of the entire epidemic has been derived. Also the partial differential equation for the moment generating function of the proportion of susceptibles in the population is established. In the end, we have studied a stochastic approach of the system.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Network epidemic models with two levels of mixing

The study of epidemics on social networks has attracted considerable attention recently. In this paper, we consider a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic on a finite network, having an arbitrary but specified degree distribution, in which individuals also make casual contacts, i.e. with people chosen uniformly from the population. The behaviour of the model as the network size tends to infinity is investigated. In particular, the basic reproduction number R(0), that governs whether or not an epidemic with few initial infectives can become established is determined, as are the probability that an epidemic becomes established and the proportion of the population who are ultimately infected by such an epidemic. For the case when the infectious period is constant and all individuals in the network have the same degree, the asymptotic variance and a central limit theorem for the size of an epidemic that becomes established are obtained. Letting the rate at which individuals make casual contacts decrease to zero yields, heuristically, corresponding results for the model without casual contacts, i.e. for the standard SIR network epidemic model. A deterministic model that approximates the spread of an epidemic that becomes established in a large population is also derived. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations work well, even for only moderately sized networks, and that the degree distribution and the inclusion of casual contacts can each have a major impact on the outcome of an epidemic.     

母猪生殖器官大小和产仔数的分子遗传基础

采用单核苷酸多态分析技术（SNP）分析母猪3个生殖激素受体基因（ESR、PRLR和FSHR）的变异,屠宰103头母猪并测定其生殖器官大小;统计母猪的产仔数;利用SAS或SPSS分析软件分析基因变异与母猪的生殖器官大小,产仔数多少的连锁关系,以探讨母猪生殖器官大小和产仔数多少的分子遗传基础,结果表明,如母猪携带的基因型为位点,ESR的BB型,位点FSHRB的BB型,位点ESRB的AA型,位点PRLR的AA型,则母猪的生殖器官较大,产仔数也较多;在位点ESRB或位点PRLR中,带有AA基因型母猪不仅产仔数显著地高于AB、BB型,而且生殖器官也显著大于AB、BB型;在位点ESR和FSHRB中,带有BB基因型母猪的生殖器官,产仔数显著高于带有AB或AA型母猪。     

Perspective: the size-complexity rule

It is widely accepted that bigger entities have a greater division of labor than smaller ones and this is reflected in the fact that larger multicellular organisms have a corresponding increase in the number of their cell types. This rule is examined in some detail from very small organisms to large animals, and plants, and societies. Compared to other size-related rules, the size-complexity rule is relatively rough and approximate, yet clearly it holds throughout the whole range of living organisms, as well as for societies. The relationship between size and complexity is analyzed by examining the effects of size increase and decrease: size increase requires an increase in complexity, whereas size decrease permits, and sometimes requires, a decrease in complexity. Conversely, an increase or decrease in complexity permits, but does not require changes in size. An especially compelling argument for the close relation between size and complexity can be found in size quorum sensing in very small multicellular organisms.     

Are flowers physiological sinks or faucets? Costs and correlates of water use by flowers of Polemonium viscosum

Water loss through inflorescences may place extreme demands on plant water status in arid environments. Here we examine how corolla size, a trait known to influence pollination success, affects the water cost of flowering in the alpine skypilot, Polemonium viscosum. In a potometry experiment, water uptake rates of inflorescences were monitored during bud expansion and anthesis. Corolla volume of fully expanded flowers predicted water uptake during bud expansion (R ²=0.61, P=0.0375) and corolla surface area predicted water uptake during anthesis (R ²=0.59, P=0.044). To probe mechanisms underlying the relationship between corolla size and water uptake, cell dimensions and densities were measured in several regions of fully expanded corollas. Corolla length was positively correlated with cell length in the middle of the corolla tube and cell diameter in the corolla lobe (Pearson's r from 0.26–0.33, n=86, P ≤ 0.05). Cell density was negatively correlated with cell dimensions in the upper corolla tube and lobe (Pearson's r from –0.39 to –0.42, P ≤ 0.0015). These findings suggest that more water may be required to maintain turgor in large corollas in part because their tissues have lower cell wall densities. The carbon cost of water use by flowers was assessed in krummholz and tundra habitats for P. viscosum flowering, respectively, during dry and wet portions of the growing season. For plants in full flower, average leaf water potentials were significantly more negative (P=0.0079) at mid-day in the krummholz (June) than in the tundra (July), but were similar before dawn (P=0.631). Photosynthetic rate at the time of flowering declined significantly with increasing corolla size in the krummholz (P=0.0376), but was unrelated to corolla size on the tundra (P>0.72). Plants losing water through large corollas may close leaf stomata to maintain turgor. If photosynthesis limits growth in this perennial species, then the water cost of producing large flowers should exacerbate the cost of reproduction under dry conditions. Such factors could select for flowers with smaller corollas in the krummholz, countering pollinator-mediated selection and helping maintain genetic variation in corolla size components of P. viscosum. Received: 5 May 1998 / Accepted: 2 October 1998     

JC病毒在中国感染状况的研究

报道了在国内5个大中城市部分非免疫功能不全,也未受过免疫抑制剂治疗人群的尿标本中,用PCR法扩增JC病毒的V－T间序列。结果证实JC病毒在中国也是广为蔓廷的病毒,并且各城市间检出率有明显差异,高者达66％（33／50）．低者仅14％（7／50）,平均为31％（78／250）。中部和南方城市的检出明显高于北方城市。大城市与中等城市,大城市与大城市郊区的检出率有显著性差异,大城市郊区与中等城市无明显差异,与国外研究结果一致。作为进行性多灶性白质脑病病原,本次在国内的检出率与国外结果相近,希望引起有关学者的关注。     

Mathematical Models for the Spread and Control of Foot-and-Mouth Disease During the 1973 Epidemic in Austria

Two models are studied to describe the spread of foot-and-mouth disease during the 1973 epidemic in Austria. The models are modifications of a three-class-model (due to KERMACK and MC KENDRICK ) taking into account the special character of the disease as well as control methods (stamping-out-method, vaccination programs).     

Fish predation on Eudiaptomus gracilis in relation to clutch size,body size,and sex: a field experiment

An enclosure experiment was performed to test for direct predationeffects on fecundity and adult body size of the copepod Eudiaptomus gracilis in the field. By introducing a high densityof fish (15 underyearling roach, Rutilus rutilus, per 350litre enclosure) and documenting the short-term effects on traitsin a rapidly decreasing prey population, responses to changes inthe phytoplankton community were minimized. After 68 hours ofpredation, clutch size and frequency of females carrying eggs weresignificantly lower in fish enclosures. Female density was moreaffected than male density. Predation selected against large bodysize in both sexes but less so in females, leading to an increasedsexual size dimorphism. The results agree with predictions based onprey selectivity in fish. Predation risk should increase withclutch size and body size since these traits increase theconspicuousness of prey. The size of the highly visible egg-clutchmay be more important than body size. Female body size wasuncorrelated to clutch size, which may explain the weaker sizeeffect among females and the changed sexual sizedimorphism.