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Knowledge on the transmission tree of an epidemic can provide valuable insights into disease dynamics. The transmission tree can be reconstructed by analysing either detailed epidemiological data (e.g. contact tracing) or, if sufficient genetic diversity accumulates over the course of the epidemic, genetic data of the pathogen. We present a likelihood-based framework to integrate these two data types, estimating probabilities of infection by taking weighted averages over the set of possible transmission trees. We test the approach by applying it to temporal, geographical and genetic data on the 241 poultry farms infected in an epidemic of avian influenza A (H7N7) in The Netherlands in 2003. We show that the combined approach estimates the transmission tree with higher correctness and resolution than analyses based on genetic or epidemiological data alone. Furthermore, the estimated tree reveals the relative infectiousness of farms of different types and sizes. [ABSTRACT FROM AUTHOR]

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number. [ABSTRACT FROM AUTHOR]

Current HPV vaccines target a subset of the oncogenic human papillomavirus (HPV) types. If HPV types compete during infection, vaccination may trigger replacement by the non-targeted types. Existing approaches to assess the risk of type replacement have focused on detecting competitive interactions between pairs of vaccine and non-vaccine types. However, methods to translate any inferred pairwise interactions into predictors of replacement have been lacking. In this paper, we develop practical predictors of type replacement in a multi-type setting, readily estimable from pre-vaccination longitudinal or cross-sectional prevalence data. The predictors we propose for replacement by individual non-targeted types take the form of weighted cross-hazard ratios of acquisition versus clearance, or aggregate odds ratios of coinfection with the vaccine types. We elucidate how the hazard-based predictors incorporate potentially heterogeneous direct and indirect type interactions by appropriately weighting type-specific hazards and show when they are equivalent to the odds-based predictors. Additionally, pooling type-specific predictors proves to be useful for predicting increase in the overall non-vaccine-type prevalence. Using simulations, we demonstrate good performance of the predictors under different interaction structures. We discuss potential applications and limitations of the proposed methodology in predicting type replacement, as compared to existing approaches. This article is part of the theme issue 'Silent cancer agents: multi-disciplinary modelling of human DNA oncoviruses'.

When controlling an emerging outbreak of an infectious disease, it is essential to know the key epidemiological parameters, such as the basic reproduction number R0 and the control effort required to prevent a large outbreak. These parameters are estimated from the observed incidence of new cases and information about the infectious contact structures of the population in which the disease spreads. However, the relevant infectious contact structures for new, emerging infections are often unknown or hard to obtain. Here, we show that, for many common true underlying heterogeneous contact structures, the simplification to neglect such structures and instead assume that all contacts are made homogeneously in the whole population results in conservative estimates for R0 and the required control effort. This means that robust control policies can be planned during the early stages of an outbreak, using such conservative estimates of the required control effort., (© 2016 The Authors.)

Obtaining a quantitative understanding of the transmission dynamics of influenza A is important for predicting healthcare demand and assessing the likely impact of intervention measures. The pandemic of 2009 provides an ideal platform for developing integrative analyses as it has been studied intensively, and a wealth of data sources is available. Here, we analyse two complementary datasets in a disease transmission framework: cross-sectional serological surveys providing data on infection attack rates, and hospitalization data that convey information on the timing and duration of the pandemic. We estimate key epidemic determinants such as infection and hospitalization rates, and the impact of a school holiday. In contrast to previous approaches, our novel modelling of serological data with mixture distributions provides a probabilistic classification of individual samples (susceptible, immune and infected), propagating classification uncertainties to the transmission model and enabling serological classifications to be informed by hospitalization data. The analyses show that high levels of immunity among persons 20 years and older provide a consistent explanation of the skewed attack rates observed during the pandemic and yield precise estimates of the probability of hospitalization per infection (1-4 years: 0.00096 (95%CrI: 0.00078-0.0012); 5-19 years: 0.00036 (0.00031-0.0044); 20-64 years: 0.0015 (0.00091-0.0020); 65+ years: 0.0084 (0.0028-0.016)). The analyses suggest that in The Netherlands, the school holiday period reduced the number of infectious contacts between 5- and 9-year-old children substantially (estimated reduction: 54%; 95%CrI: 29-82%), thereby delaying the unfolding of the pandemic in The Netherlands by approximately a week.

Sizeable quantities of 2009 pandemic influenza A/H1N1 (H1N1pdm) vaccine in the USA became available at the end of 2009 when the autumn wave of the epidemic was declining. At that point, risk factors for H1N1-related mortality for some of the high-risk groups, particularly adults with underlying health conditions, could be estimated. Although those high-risk groups are natural candidates for being in the top priority tier for vaccine allocation, another candidate group is school-aged children through their role as vectors for transmission affecting the whole community. In this paper, we investigate the question of prioritization for vaccine allocation in a declining epidemic between two groups-a group with a high risk of mortality versus a 'core' group with a relatively low risk of mortality but fuelling transmission in the community. We show that epidemic data can be used, under certain assumptions on future decline, seasonality and vaccine efficacy in different population groups, to give a criterion when initial prioritization of a population group with a sufficiently high risk of epidemic-associated mortality is advisable over the policy of prioritizing the core group.

Measles is a highly infectious disease that has been targeted for elimination from four WHO regions. Whether and under which conditions this goal is feasible is, however, uncertain since outbreaks have been documented in populations with high vaccination coverage (more than 90%). Here, we use the example of a large outbreak in a German public school to show how estimates of key epidemiological parameters such as the basic reproduction number (R(0)), vaccine efficacy (VE(S)) and critical vaccination coverage (p(c)) can be obtained from partially observed outbreaks in highly vaccinated populations. Our analyses rely on Bayesian methods of inference based on the final size distribution of outbreak size, and use data which are easily collected. For the German public school the analyses indicate that the basic reproduction number of measles is higher than previously thought (R(0) = 30.8, 95% credible interval: 23.6-40.4), that the vaccine is highly effective in preventing infection (VE(S) = 0.997, 95% credible interval: 0.993-0.999), and that a vaccination coverage in excess of 95 per cent may be necessary to achieve herd immunity (p(c) = 0.971, 95% credible interval: 0.961-0.978). We discuss the implications for measles elimination from highly vaccinated populations.

We describe a prioritization scheme for an allocation of a sizeable quantity of vaccine or antivirals in a stratified population. The scheme builds on an optimal strategy for reducing the epidemic's initial growth rate in a stratified mass-action model. The strategy is tested on the EpiSims network describing interactions and influenza dynamics in the population of Utah, where the stratification we have chosen is by age (0-6, 7-13, 14-18, adults). No prior immunity information is available, thus everyone is assumed to be susceptible-this may be relevant, possibly with the exception of persons over 50, to the 2009 H1N1 influenza outbreak. We have found that the top priority in an allocation of a sizeable quantity of seasonal influenza vaccinations goes to young children (0-6), followed by teens (14-18), then children (7-13), with the adult share being quite low. These results, which rely on the structure of the EpiSims network, are compared with the current influenza vaccination coverage levels in the US population.

The reporting interval of infectious diseases is often determined as a time unit in the calendar regardless of the epidemiological characteristics of the disease. No guidelines have been proposed to choose the reporting interval of infectious diseases. The present study aims at translating coarsely reported epidemic data into the reproduction number and clarifying the ideal reporting interval to offer detailed insights into the time course of an epidemic. We briefly revisit the dispersibility ratio, i.e. ratio of cases in successive reporting intervals, proposed by Clare Oswald Stallybrass, detecting technical flaws in the historical studies. We derive a corrected expression for this quantity and propose simple algorithms to estimate the effective reproduction number as a function of time, adjusting the reporting interval to the generation time of a disease and demonstrating a clear relationship among the generation-time distribution, reporting interval and growth rate of an epidemic. Our exercise suggests that an ideal reporting interval is the mean generation time, so that the ratio of cases in successive intervals can yield the reproduction number. When it is impractical to report observations every mean generation time, we also present an alternative method that enables us to obtain straightforward estimates of the reproduction number for any reporting interval that suits the practical purpose of infection control.