Protocols for sampling viral sequences to study epidemic dynamics

With more emphasis being put on global infectious disease monitoring, viral genetic data are being collected at an astounding rate, both within and without the context of a long-term disease surveillance plan. Concurrent with this increase have come improvements to the sophisticated and generalized statistical techniques used for extracting population-level information from genetic sequence data. However, little research has been done on how the collection of these viral sequence data can or does affect the efficacy of the phylogenetic algorithms used to analyse and interpret them. In this study, we use epidemic simulations to consider how the collection of viral sequence data clarifies or distorts the picture, provided by the phylogenetic algorithms, of the underlying population dynamics of the simulated viral infection over many epidemic cycles. We find that sampling protocols purposefully designed to capture sequences at specific points in the epidemic cycle, such as is done for seasonal influenza surveillance, lead to a significantly better view of the underlying population dynamics than do less-focused collection protocols. Our results suggest that the temporal distribution of samples can have a significant effect on what can be inferred from genetic data, and thus highlight the importance of considering this distribution when designing or evaluating protocols and analysing the data collected thereunder.     

Inferring environmental transmission using phylodynamics: a case-study using simulated evolution of an enteric pathogen

Indirect (environmental) and direct (host–host) transmission pathways cannot easily be distinguished when they co-occur in epidemics, particularly when they occur on similar time scales. Phylodynamic reconstruction is a potential approach to this problem that combines epidemiological information (temporal, spatial information) with pathogen whole-genome sequencing data to infer transmission trees of epidemics. However, factors such as differences in mutation and transmission rates between host and non-host environments may obscure phylogenetic inference from these methods. In this study, we used a network-based transmission model that explicitly models pathogen evolution to simulate epidemics with both direct and indirect transmission. Epidemics were simulated according to factorial combinations of direct/indirect transmission proportions, host mutation rates and conditions of environmental pathogen growth. Transmission trees were then reconstructed using the phylodynamic approach SCOTTI (structured coalescent transmission tree inference) and evaluated. We found that although insufficient diversity sets a lower bound on when accurate phylodynamic inferences can be made, transmission routes and assumed pathogen lifestyle affected pathogen population structure and subsequently influenced both reconstruction success and the likelihood of direct versus indirect pathways being reconstructed. We conclude that prior knowledge of the likely ecology and population structure of pathogens in host and non-host environments is critical to fully using phylodynamic techniques.     

Inferring the reproduction number using the renewal equation in heterogeneous epidemics

Real-time estimation of the reproduction number has become the focus of modelling groups around the world as the SARS-CoV-2 pandemic unfolds. One of the most widely adopted means of inference of the reproduction number is via the renewal equation, which uses the incidence of infection and the generation time distribution. In this paper, we derive a multi-type equivalent to the renewal equation to estimate a reproduction number which accounts for heterogeneity in transmissibility including through asymptomatic transmission, symptomatic isolation and vaccination. We demonstrate how use of the renewal equation that misses these heterogeneities can result in biased estimates of the reproduction number. While the bias is small with symptomatic isolation, it can be much larger with asymptomatic transmission or transmission from vaccinated individuals if these groups exhibit substantially different generation time distributions to unvaccinated symptomatic transmitters, whose generation time distribution is often well defined. The bias in estimate becomes larger with greater population size or transmissibility of the poorly characterized group. We apply our methodology to Ebola in West Africa in 2014 and the SARS-CoV-2 in the UK in 2020–2021.     

Inferring social network structure in ecological systems from spatio-temporal data streams

We propose a methodology for extracting social network structure from spatio-temporal datasets that describe timestamped occurrences of individuals. Our approach identifies temporal regions of dense agent activity and links are drawn between individuals based on their co-occurrences across these ‘gathering events’. The statistical significance of these connections is then tested against an appropriate null model. Such a framework allows us to exploit the wealth of analytical and computational tools of network analysis in settings where the underlying connectivity pattern between interacting agents (commonly termed the adjacency matrix) is not given a priori. We perform experiments on two large-scale datasets (greater than 10⁶ points) of great tit Parus major wild bird foraging records and illustrate the use of this approach by examining the temporal dynamics of pairing behaviour, a process that was previously very hard to observe. We show that established pair bonds are maintained continuously, whereas new pair bonds form at variable times before breeding, but are characterized by a rapid development of network proximity. The method proposed here is general, and can be applied to any system with information about the temporal co-occurrence of interacting agents.     

Inferring phase diagrams from X-ray data with background signals using graph segmentation

Automated composition-structure-processing phase diagram creation is critical for high-throughput experimental material studies. In particular, diffractogram datasets with large background signals are especially difficult to identify the phase regions. In this work, we proposed a novel graph segmentation algorithm from computer vision to solve the phase diagram prediction problem from X-ray diffraction data with large background signals. We introduced a novel background subtraction algorithm with graph-based clustering/segmentation to build the BGPhase algorithm. Experiments on three datasets with the Al–Cu–Mo material family showed that our phase attribution algorithm can achieve high prediction accuracy ranging from 88.6 to 94.8% or with MCC scores ranging from 0.715 to 0.890. The algorithm can be accessed online at http://mleg.cse.sc.edu/bgphase.     

Comparative estimation of the reproduction number for pandemic influenza from daily case notification data

The reproduction number, R, defined as the average number of secondary cases generated by a primary case, is a crucial quantity for identifying the intensity of interventions required to control an epidemic. Current estimates of the reproduction number for seasonal influenza show wide variation and, in particular, uncertainty bounds for R for the pandemic strain from 1918 to 1919 have been obtained only in a few recent studies and are yet to be fully clarified. Here, we estimate R using daily case notifications during the autumn wave of the influenza pandemic (Spanish flu) in the city of San Francisco, California, from 1918 to 1919. In order to elucidate the effects from adopting different estimation approaches, four different methods are used: estimation of R using the early exponential-growth rate (Method 1), a simple susceptible-exposed-infectious-recovered (SEIR) model (Method 2), a more complex SEIR-type model that accounts for asymptomatic and hospitalized cases (Method 3), and a stochastic susceptible-infectious-removed (SIR) with Bayesian estimation (Method 4) that determines the effective reproduction number Rt at a given time t. The first three methods fit the initial exponential-growth phase of the epidemic, which was explicitly determined by the goodness-of-fit test. Moreover, Method 3 was also fitted to the whole epidemic curve. Whereas the values of R obtained using the first three methods based on the initial growth phase were estimated to be 2.98 (95% confidence interval (CI): 2.73, 3.25), 2.38 (2.16, 2.60) and 2.20 (1.55, 2.84), the third method with the entire epidemic curve yielded a value of 3.53 (3.45, 3.62). This larger value could be an overestimate since the goodness-of-fit to the initial exponential phase worsened when we fitted the model to the entire epidemic curve, and because the model is established as an autonomous system without time-varying assumptions. These estimates were shown to be robust to parameter uncertainties, but the theoretical exponential-growth approximation (Method 1) shows wide uncertainty. Method 4 provided a maximum-likelihood effective reproduction number 2.10 (1.21, 2.95) using the first 17 epidemic days, which is consistent with estimates obtained from the other methods and an estimate of 2.36 (2.07, 2.65) for the entire autumn wave. We conclude that the reproduction number for pandemic influenza (Spanish flu) at the city level can be robustly assessed to lie in the range of 2.0-3.0, in broad agreement with previous estimates using distinct data.     

Scatter bands in creep and fatigue crack growth rates in high temperature plant materials data

As a part of the European Commission supported project BE 1702: ‘HIDA’ Creep, creep-fatigue and high temperature fatigue crack growth data for five high temperature plant steels were accessed from a number of published and unpublished sources. These large sets of data were reviewed, and re-analysed where necessary, and plotted in terms of various crack growth rate correlating parameters. Thus limits of scatter bands and mean and upper 95% confidence limit creep and fatigue crack growth correlations are proposed. The present work covers a wide range of variables such as test specimen geometries, sizes, loading conditions and temperatures. Therefore, the correlations proposed are considered universal. However, it is envisaged that these correlations will be refined in future by enlarging the database and exploring the effect of the variables described above. The five materials studied are AISI 316 stainless, 2.25CrlMo, P91, 1CrMoV (forged), and 1CrMoV (cast) steel.     

Estimating antiviral effectiveness against pandemic influenza using household data

Current estimates of antiviral effectiveness for influenza are based on the existing strains of the virus. Should a pandemic strain emerge, strain-specific estimates will be required as early as possible to ensure that antiviral stockpiles are used optimally and to compare the benefits of using antivirals as prophylaxis or to treat cases. We present a method to measure antiviral effectiveness using early pandemic data on household outbreak sizes, including households that are provided with antivirals for prophylaxis and those provided with antivirals for treatment only. We can assess whether antiviral drugs have a significant impact on susceptibility or on infectivity with the data from approximately 200 to 500 households with a primary case. Fewer households will suffice if the data can be collected before case numbers become high, and estimates are more precise if the study includes data from prophylaxed households and households where no antivirals are provided. Rates of asymptomatic infection and the level of transmissibility of the virus do not affect the accuracy of these estimates greatly, but the pattern of infectivity in the individual strongly influences the estimate of the effect of antivirals on infectivity. An accurate characterization of the infectiousness profile—informed by strain-specific data—is essential for measuring antiviral effectiveness.     

Likelihood-based estimation of continuous-time epidemic models from time-series data: application to measles transmission in London

We present a new statistical approach to analyse epidemic time-series data. A major difficulty for inference is that (i) the latent transmission process is partially observed and (ii) observed quantities are further aggregated temporally. We develop a data augmentation strategy to tackle these problems and introduce a diffusion process that mimics the susceptible-infectious-removed (SIR) epidemic process, but that is more tractable analytically. While methods based on discrete-time models require epidemic and data collection processes to have similar time scales, our approach, based on a continuous-time model, is free of such constraint. Using simulated data, we found that all parameters of the SIR model, including the generation time, were estimated accurately if the observation interval was less than 2.5 times the generation time of the disease. Previous discrete-time TSIR models have been unable to estimate generation times, given that they assume the generation time is equal to the observation interval. However, we were unable to estimate the generation time of measles accurately from historical data. This indicates that simple models assuming homogenous mixing (even with age structure) of the type which are standard in mathematical epidemiology miss key features of epidemics in large populations.     

Prediction of invasion from the early stage of an epidemic

Predictability of undesired events is a question of great interest in many scientific disciplines including seismology, economy and epidemiology. Here, we focus on the predictability of invasion of a broad class of epidemics caused by diseases that lead to permanent immunity of infected hosts after recovery or death. We approach the problem from the perspective of the science of complexity by proposing and testing several strategies for the estimation of important characteristics of epidemics, such as the probability of invasion. Our results suggest that parsimonious approximate methodologies may lead to the most reliable and robust predictions. The proposed methodologies are first applied to analysis of experimentally observed epidemics: invasion of the fungal plant pathogen Rhizoctonia solani in replicated host microcosms. We then consider numerical experiments of the susceptible–infected–removed model to investigate the performance of the proposed methods in further detail. The suggested framework can be used as a valuable tool for quick assessment of epidemic threat at the stage when epidemics only start developing. Moreover, our work amplifies the significance of the small-scale and finite-time microcosm realizations of epidemics revealing their predictive power.     

The calculation of growth and nucleation kinetics from MSMPR crystallizer data including growth rate dispersion

One of the most important applications of the population balance approach to crystallizer modeling is the recovery of crystal nucleation and growth rate data from steady state crystal size distributions as described by Randolph and Larson in 1971. Recent crystallization studies have revealed that growth rate dispersion, wherein crystals of the same size do not have the same growth rate, causes nonidealities that limit the usefulness of the Randolph and Larson approach. The present work presents and shows application of a procedure that allows calculation of unambiguous nucleation and growth rate kinetics in the presence of growth rate dispersion. It requires the appropriate choice of growth rate distribution for a fit to the experimental data. The method is applied to analysis of pilot scale crystallization experiments with the sucrose-water system and indicates that unimodal distributions may be incapable of describing such data.     

Small crack growth rates from simple sequences containing underloads in AA7050-T7451

Fatigue crack growth in materials that display confined slip show crack path changes that are dependant on the loading history. In these materials certain variable amplitude loading patterns can produce strong slip bands ahead of the crack tip. One of these patterns of loadings involving bands of high R cycles followed by one or two underloads also produce distinct features or progression marks on the fracture surface that have been used to delimit small blocks of constant amplitude cycles. The same loading pattern also produces strong slip bands ahead of the fatigue crack both in the plane of the crack and out of plane. These slip bands affect the direction and possibly the rate of propagation of the fatigue crack. Thus these loading patterns make an ideal marker to look at small crack growth rates in the presence of slip bands.This paper reports on the crack growth rates for a series of fatigue cracks grown in AA7050-T7451 coupons, from near initiation to near failure. The aim of this work was to generate constant amplitude crack growth data for use in predictions that is more useful for predicting crack growth lives than that obtained from long crack constant amplitude tests. Three simple sequences which applied small bands of constant amplitude loading were used in the fatigue tests preceded by a loading sequence to produce a progression mark to delimit the bands. The fatigue cracks in the coupon initiated from etch pits on the surface of the coupons. The width of the bands of constant amplitude growth in these sequences were measured under a microscope. The growth in these sequences was found to be faster than for long cracks under constant amplitude loading.     

The extraction of ionic conductivities and hopping rates from a.c. conductivity data

Over a wide range of frequencies, the a.c. conductivity of ionic materials shows two regions of frequency-dependent conductivity. These are each characterized by a term K _p ^{1–n n} where K, n are constants, _p is a fundamental frequency identified with the hopping rate and is the measuring frequency. This behaviour is an example of Jonscher's Law of Dielectric Response for ionic conductors. In many cases, the region of low-frequency dispersion approximates to a frequency-independent plateau which may be taken as the d.c. conductivity. In others, a significant low-frequency dispersion is present and cannot be ignored in determining the effective d.c. conductivity. A method for the extraction of d.c. conductivities, hopping rates and for estimating carrier concentration effects is described. Data for three different types of material, single-crystal LiGaO₂, -alumina and Na/Ag -alumina are used to illustrate the method.