The tracking and projection of emerging epidemics is hindered by the disconnect between apparent epidemic dynamics, discernible from noisy and incomplete surveillance data, and the underlying, imperfectly observed, system. Behavior changes compound this, altering both true dynamics and reporting patterns, particularly for diseases with nonspecific symptoms, such as influenza. We disentangle these effects to unravel the hidden dynamics of the 2009 influenza A/H1N1pdm pandemic in London, where surveillance suggests an unusual dominant peak in the summer. We embed an age-structured model into a Bayesian synthesis of multiple evidence sources to reveal substantial changes in contact patterns and health-seeking behavior throughout the epidemic, uncovering two similar infection waves, despite large differences in the reported levels of disease. We show how this approach, which allows for real-time learning about model parameters as the epidemic progresses, is also able to provide a sequence of nested projections that are capable of accurately reflecting the epidemic evolution.Bayesian statistics | real-time modeling | general practice consultation data | infectious disease | seroepidemiology A n emerging epidemic engenders an increased demand upon health services. Resolving the extent to which this is due to high levels of disease transmission as opposed to a heightened public sensitivity is essential for determining the appropriate public health response.This was especially crucial when estimating the course of the 2009 influenza A/H1N1pdm outbreak in England, where, unusually, the pandemic resulted in a summer peak in rates of consultation at general practices (GPs) for influenza-like illness (ILI). This is clearly demonstrated by data from the return service of the Royal College of General Practitioners (RCGP) in Fig. 1A where weekly GP consultation rates per 100,000 population over the 2009 pandemic are compared with rates from the three previous years. Also shown is the proportion of swabbed individuals whose swabs tested positive for the presence of any flu virus (SI Data). Note that the GP consultation rate for 2009 is much higher than the usual seasonal rate, whereas the corresponding positivity is comparable to that observed in the preceding winters. This suggests that a substantial proportion of the peak in consultations was not directly attributable to A/H1N1pdm. Conversely, serological studies (3) have shown a marked increase in the prevalence of influenza antibodies among the population. Therefore, the degree to which the increased demand upon GPs is due to high levels of disease transmission as opposed to heightened public sensitivity remains unclear (4). Fig. 1 B and C show GP consultation rates by region and age group: consultations in Greater London and the West Midlands exhibit rapid early exponential growth, but the peak in London is much higher; rates appear to decrease markedly with age. Importantly, a first peak occurs immediately prior to the summer school holiday and the launch of the National ...

In standard models of quantitative traits, genotypes are assumed to differ in mean but not variance of the trait. Here we consider directional selection for a quantitative trait for which genotypes also confer differences in variability, viewed either as differences in residual phenotypic variance when individual loci are concerned or as differences in environmental variability when the whole genome is considered. At an individual locus with additive effects, the selective value of the increasing allele is given by ia/sigma + 1/2 ixb/sigma2, where i is the selection intensity, x is the standardized truncation point, sigma2 is the phenotypic variance, and a/sigma and b/sigma2 are the standardized differences in mean and variance respectively between genotypes at the locus. Assuming additive effects on mean and variance across loci, the response to selection on phenotype in mean is isigma2(Am)/sigma + 1/2 ixcov(Amv)/sigma2 and in variance is icov(Amv)/sigma + 1/2 ixsigma2(Av)/sigma2, where sigma2(Am) is the (usual) additive genetic variance of effects of genes on the mean, sigma2(Av) is the corresponding additive genetic variance of their effects on the variance, and cov(Amv) is the additive genetic covariance of their effects. Changes in variance also have to be corrected for any changes due to gene frequency change and for the Bulmer effect, and relevant formulae are given. It is shown that effects on variance are likely to be greatest when selection is intense and when selection is on individual phenotype or within family deviation rather than on family mean performance. The evidence for and implications of such variability in variance are discussed.

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Analyses of effects of mutants on many traits have enabled estimates to be obtained of the magnitude of pleiotropy, and in reviews of such data others have concluded that the degree of pleiotropy is highly restricted, with implications on the evolvability of complex organisms. We show that these conclusions are highly dependent on statistical assumptions, for example significance levels. We analyze models with pleiotropic effects on all traits at all loci but by variable amounts, considering distributions of numbers of traits declared significant, overall pleiotropic effects, and extent of apparent modularity of effects. We demonstrate that these highly pleiotropic models can give results similar to those obtained in analyses of experimental data and that conclusions on limits to evolvability through pleiotropy are not robust. BIOLOGICAL organisms are complex structures, so it is not surprising that their genes often show pleiotropic effects over two or more traits. Evidence comes both from observations on substitutions at individual loci and from genetic correlations among the traits at a population level. One view is that all genes are fully pleiotropic, at least at the quantitative level, in view of the highly interdependent and interactive nature of biological systems. Another view is that such an argument is irrelevant to genetic understanding, analysis, and application in that most loci are likely to affect no more than a small minority of traits in any biologically significant way (Stearns 2010).The general degree of pleiotropy is important in several areas, for example in understanding pathways of gene action, in assessing potential side effects of genetic manipulation of particular pathways, in assessing the impacts of selective genetic improvement programs, and in considering the opportunities for evolutionary change through new mutations that may induce both favorable and unfavorable effects on fitness.In a recent perspectives paper Wagner and Zhang (2011) discuss the magnitude of pleiotropy for complex or quantitative traits. They argue that it is highly restricted, i.e., rather few traits are influenced by each gene, and consequently conclude there is more opportunity for evolutionary change according to Fisher's (1930) geometric model than suggested by the analyses of Orr (2000) and for finding drugs specific for a particular genetic disease.Different kinds of data sets were used by Wagner and Zhang, many of them collected by them and their colleagues. One is based on mapping QTL using F 2 crosses of selected lines of mice (Wagner et al. 2008), but pleiotropy and linkage of nonpleiotropic QTL cannot readily be disentangled. The other is based on single mutant lines where this complication does not arise. Wang et al. (2010) analyzed four published data sets on mutants, two of which were very large: One included 253 morphological traits, each recorded on 2449 haploid lines of Saccharomyces cerevisiae, each mutant for a different gene. The mean number of traits affected by each line was 21.6...

Background: Households appear to be the highest risk setting for transmission of COVID-19. Large household transmission studies were reported in the early stages of the pandemic in Asia with secondary attack rates ranging from 5-30% but few large scale household transmission studies have been conducted outside of Asia. Methods: A prospective case ascertained study design based on the World Health Organization FFX protocol was undertaken in the UK following the detection of the first case in late January 2020. Household contacts of cases were followed using enhanced surveillance forms to establish whether they developed symptoms of COVID-19, became confirmed cases and their outcomes. Household secondary attack rates and serial intervals were estimated. Individual and household basic reproduction numbers were also estimated. The incubation period was estimated using known point source exposures that resulted in secondary cases. Results: A total of 233 households with two or more people were included with a total of 472 contacts. The overall household SAR was 37% (95% CI 31-43%) with a mean serial interval of 4.67 days, an R0 of 1.85 and a household reproduction number of 2.33. We find lower secondary attack rates in larger households. SARs were highest when the primary case was a child. We estimate a mean incubation period of around 4.5 days. Conclusions: High rates of household transmission of COVID-19 were found in the UK emphasising the need for preventative measures in this setting. Careful monitoring of schools reopening is needed to monitor transmission from children.

We investigate maintenance of quantitative genetic variation at mutation-selection balance for multiple traits. The intrinsic strength of real stabilizing selection on one of these traits denoted the "target trait" and the observed strength of apparent stabilizing selection on the target trait can be quite different: the latter, which is estimable, is much smaller (i.e., implying stronger selection) than the former. Distinguishing them may enable the mutation load to be relaxed when considering multivariate stabilizing selection. It is shown that both correlations among mutational effects and among strengths of real stabilizing selection on the traits are not important unless they are high. The analysis for independent situations thus provides a good approximation to the case where mutant and stabilizing selection effects are correlated. Multivariate stabilizing selection can be regarded as a combination of stabilizing selection on the target trait and the pleiotropic direct selection on fitness that is solely due to the effects of real stabilizing selection on the hidden traits. As the overall fitness approaches a constant value as the number of traits increases, multivariate stabilizing selection can maintain abundant genetic variance only under quite weak selection. The common observations of high polygenic variance and strong stabilizing selection thus imply that if the mutation-selection balance is the true mechanism of maintenance of genetic variation, the apparent stabilizing selection cannot arise solely by real stabilizing selection simultaneously on many metric traits.

Identifying risk factors for the presence of Escherichia coli O157 infection on cattle farms is important for understanding the epidemiology of this zoonotic infection in its main reservoir and for informing the design of interventions to reduce the public health risk. Here, we use data from a large-scale field study carried out in Scotland to fit both “SIS”-type dynamical models and statistical risk factor models. By comparing the fit (assessed using maximum likelihood) of different dynamical models we are able to identify the most parsimonious model (using the AIC statistic) and compare it with the model suggested by risk factor analysis. Both approaches identify 2 key risk factors: the movement of cattle onto the farm and the number of cattle on the farm. There was no evidence for a role of other livestock species or seasonality, or of significant risk of local spread. However, the most parsimonious dynamical model does predict that farms can infect other farms through routes other than cattle movement, and that there is a nonlinear relationship between the force of infection and the number of infected farms. An important prediction from the most parsimonious model is that although only ∼ 20% farms may harbour E. coli O157 infection at any given time ∼ 80% may harbour infection at some point during the course of a year.

In models of maintenance of genetic variance (V G ) it has often been assumed that mutant alleles act additively. However, experimental data show that the dominance coefficient varies among mutant alleles and those of large effect tend to be recessive. On the basis of empirical knowledge of mutations, a jointeffect model of pleiotropic and real stabilizing selection that includes dominance is constructed and analyzed. It is shown that dominance can dramatically alter the prediction of equilibrium V G . Analysis indicates that for the situations where mutations are more recessive for fitness than for a quantitative trait, as supported by the available data, the joint-effect model predicts a significantly higher V G than does an additive model. Importantly, for what seem to be realistic distributions of mutational effects (i.e., many mutants may not affect the quantitative trait substantially but are likely to affect fitness), the observed high levels of genetic variation in the quantitative trait under strong apparent stabilizing selection can be generated. This investigation supports the hypothesis that most V G comes from the alleles nearly neutral for fitness in heterozygotes while apparent stabilizing selection is contributed mainly by the alleles of large effect on the quantitative trait. Thus considerations of dominance coefficients of mutations lend further support to our previous conclusion that mutation-selection balance is a plausible mechanism of the maintenance of the genetic variance in natural populations. G ENETIC variation in quantitative traits is a ubiqui-Falconer and Mackay 1996, Chap. 20; Bü rger 2000; Barton and Keightley 2002). In classical models it is tous phenomenon. As the only ultimate source of genetic variation, mutations change their carriers' valassumed that natural selection acts either directly on the metric trait (i.e., real stabilizing selection; Kimura ues of both the metric trait and fitness. That is, muta-1965; Turelli 1984; Bü rger 2000) or on the mutant tions input fresh polygenic variance into the population genes that affect both the trait and fitness (i.e., pure and at the same time put the population under selection pleiotropic selection; Barton 1990; Keightley and by decreasing their carriers' fitness to a varying extent.Hill 1990; Kondrashov and Turelli 1992). Assuming These conflicting effects of mutations appear to suggest that the metric trait is not neutral and undergoes real small genetic variation. However, high levels of genetic stabilizing selection, nevertheless, a model in which variance (V G ; i.e., a heritability in the range 25-50%) pleiotropic and real stabilizing selections are combined are observed typically in natural populations for quantican induce significant stabilizing selection as well as tative traits, and it has usually been assumed that traits substantial genetic variance . are under strong stabilizing selection, with apparent However, it still has difficulty in accounting for the obstrength (V s,t ) ‫02ف‬V e (Turelli 1984; Endler 198...