Scalable relaxed clock phylogenetic dating

Molecular clock models relate observed genetic diversity to calendar time, enabling estimation of times of common ancestry. Many large datasets of fast-evolving viruses are not well fitted by molecular clock models that assume a constant substitution rate through time, and more flexible relaxed clock models are required for robust inference of rates and dates. Estimation of relaxed molecular clocks using Bayesian Markov chain Monte Carlo is computationally expensive and may not scale well to large datasets. We build on recent advances in maximum likelihood and least-squares phylogenetic and molecular clock dating methods to develop a fast relaxed-clock method based on a Gamma-Poisson mixture model of substitution rates. This method estimates a distinct substitution rate for every lineage in the phylogeny while being scalable to large phylogenies. Unknown lineage sample dates can be estimated as well as unknown root position. We estimate confidence intervals for rates, dates, and tip dates using parametric and non-parametric bootstrap approaches. This method is implemented as an open-source R package, treedater

Comparison of cluster-based and source-attribution methods for estimating transmission risk using large HIV sequence databases

Phylogenetic clustering of HIV sequences from a random sample of patients can reveal epidemiological transmission patterns, but interpretation is hampered by limited theoretical support and statistical properties of clustering analysis remain poorly understood. Alternatively, source attribution methods allow fitting of HIV transmission models and thereby quantify aspects of disease transmission. A simulation study was conducted to assess error rates of clustering methods for detecting transmission risk factors. We modeled HIV epidemics among men having sex with men and generated phylogenies comparable to those that can be obtained from HIV surveillance data in the UK. Clustering and source attribution approaches were applied to evaluate their ability to identify patient attributes as transmission risk factors. We find that commonly used methods show a misleading association between cluster size or odds of clustering and covariates that are correlated with time since infection, regardless of their influence on transmission. Clustering methods usually have higher error rates and lower sensitivity than source attribution method for identifying transmission risk factors. But neither methods provide robust estimates of transmission risk ratios. Source attribution method can alleviate drawbacks from phylogenetic clustering but formal population genetic modeling may be required to estimate quantitative transmission risk factors

Comparison of cluster-based and source-attribution methods for estimating transmission risk using large HIV sequence databases

Phylogenetic clustering of HIV sequences from a random sample of patients can reveal epidemiological transmission patterns, but interpretation is hampered by limited theoretical support and statistical properties of clustering analysis remain poorly understood. Alternatively, source attribution methods allow fitting of HIV transmission models and thereby quantify aspects of disease transmission. A simulation study was conducted to assess error rates of clustering methods for detecting transmission risk factors. We modeled HIV epidemics among men having sex with men and generated phylogenies comparable to those that can be obtained from HIV surveillance data in the UK. Clustering and source attribution approaches were applied to evaluate their ability to identify patient attributes as transmission risk factors. We find that commonly used methods show a misleading association between cluster size or odds of clustering and covariates that are correlated with time since infection, regardless of their influence on transmission. Clustering methods usually have higher error rates and lower sensitivity than source attribution method for identifying transmission risk factors. But neither methods provide robust estimates of transmission risk ratios. Source attribution method can alleviate drawbacks from phylogenetic clustering but formal population genetic modeling may be required to estimate quantitative transmission risk factors

Edge-Based Compartmental Modeling for Infectious Disease Spread Part III: Disease and Population Structure

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of the disease or population from the simplistic assumptions of Part I. We allow the population to have structure due to effects such as demographic detail or multiple types of risk behavior the disease to have more complicated natural history. We introduce these modifications in the static network context, though it is straightforward to incorporate them into dynamic networks. We also consider serosorting, which requires using the dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics

Probing empirical contact networks by simulation of spreading dynamics

Disease, opinions, ideas, gossip, etc. all spread on social networks. How these networks are connected (the network structure) influences the dynamics of the spreading processes. By investigating these relationships one gains understanding both of the spreading itself and the structure and function of the contact network. In this chapter, we will summarize the recent literature using simulation of spreading processes on top of empirical contact data. We will mostly focus on disease simulations on temporal proximity networks -- networks recording who is close to whom, at what time -- but also cover other types of networks and spreading processes. We analyze 29 empirical networks to illustrate the methods

Comparison of contact patterns relevant for transmission of respiratory pathogens in Thailand and the Netherlands using respondent-driven sampling

Understanding infection dynamics of respiratory diseases requires the identification and quantification of behavioural, social and environmental factors that permit the transmission of these infections between humans. Little empirical information is available about contact patterns within real-world social networks, let alone on differences in these contact networks between populations that differ considerably on a socio-cultural level. Here we compared contact network data that were collected in the Netherlands and Thailand using a similar online respondent-driven method. By asking participants to recruit contact persons we studied network links relevant for the transmission of respiratory infections. We studied correlations between recruiter and recruited contacts to investigate mixing patterns in the observed social network components. In both countries, mixing patterns were assortative by demographic variables and random by total numbers of contacts. However, in Thailand participants reported overall more contacts which resulted in higher effective contact rates. Our findings provide new insights on numbers of contacts and mixing patterns in two different populations. These data could be used to improve parameterisation of mathematical models used to design control strategies. Although the spread of infections through populations depends on more factors, found similarities suggest that spread may be similar in the Netherlands and Thailand

Fast variables determine the epidemic threshold in the pairwise model with an improved closure

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks exhibiting degree heterogeneity, directed and/or weighted links and clustering. However, extra features of the disease dynamics or of the network lead to an increase in system size and analytical tractability becomes problematic. Various `closures' can be used to keep the system tractable. Focusing on SIR epidemics on regular but clustered networks, we show that even for the most complex closure we can determine the epidemic threshold as an asymptotic expansion in terms of the clustering coefficient.We do this by exploiting the presence of a system of fast variables, specified by the correlation structure of the epidemic, whose steady state determines the epidemic threshold. While we do not find the steady state analytically, we create an elegant asymptotic expansion of it. We validate this new threshold by comparing it to the numerical solution of the full system and find excellent agreement over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. The technique carries over to pairwise models with other closures [1] and we note that the epidemic threshold will be model dependent. This emphasises the importance of model choice when dealing with realistic outbreaks

Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks

Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To understand the joint effects of these two network properties on epidemic dynamics, the effective degree model of Lindquist et al. [28] is reformulated with a new moment closure to apply to highly clustered networks. A simulation study comparing alternative ODE models and stochastic simulations is performed for SIR (Susceptible–Infected–Removed) epidemic dynamics, including a test for the conjectured error behaviour in [40], providing evidence that this novel model can be a more accurate approximation to epidemic dynamics on complex networks than existing approaches

Cavity Induced Interfacing of Atoms and Light

This chapter introduces cavity-based light-matter quantum interfaces, with a single atom or ion in strong coupling to a high-finesse optical cavity. We discuss the deterministic generation of indistinguishable single photons from these systems; the atom-photon entanglement intractably linked to this process; and the information encoding using spatio-temporal modes within these photons. Furthermore, we show how to establish a time-reversal of the aforementioned emission process to use a coupled atom-cavity system as a quantum memory. Along the line, we also discuss the performance and characterisation of cavity photons in elementary linear-optics arrangements with single beam splitters for quantum-homodyne measurements.Comment: to appear as a book chapter in a compilation "Engineering the Atom-Photon Interaction" published by Springer in 2015, edited by A. Predojevic and M. W. Mitchel