Background The COVID-19 pandemic both relied and placed significant burdens on the experts involved from research and public health sectors. The sustained high pressure of a pandemic on responders, such as healthcare workers, can lead to lasting psychological impacts including acute stress disorder, post-traumatic stress disorder, burnout, and moral injury, which can impact individual wellbeing and productivity. Methods As members of the infectious disease modelling community, we convened a reflective workshop to understand the professional and personal impacts of response work on our community and to propose recommendations for future epidemic responses. The attendees represented a range of career stages, institutions, and disciplines. This piece was collectively produced by those present at the session based on our collective experiences. Results Key issues we identified at the workshop were lack of institutional support, insecure contracts, unequal credit and recognition, and mental health impacts. Our recommendations include rewarding impactful work, fostering academia-public health collaboration, decreasing dependence on key individuals by developing teams, increasing transparency in decision-making, and implementing sustainable work practices. Conclusions Despite limitations in representation, this workshop provided valuable insights into the UK COVID-19 modelling experience and guidance for future public health crises. Recognising and addressing the issues highlighted is crucial, in our view, for ensuring the effectiveness of epidemic response work in the future.

How likely is it to become infected by SARS-CoV-2 after being exposed? Almost everyone wondered about this question during the COVID-19 pandemic. Contact-tracing apps1,2 recorded measurements of proximity3 and duration between nearby smartphones. Contacts-individuals exposed to confirmed cases-were notified according to public health policies such as the 2 m, 15 min guideline4,5, despite limited evidence supporting this threshold. Here we analysed 7 million contacts notified by the National Health Service COVID-19 app6,7 in England and Wales to infer how app measurements translated to actual transmissions. Empirical metrics and statistical modelling showed a strong relation between app-computed risk scores and actual transmission probability. Longer exposures at greater distances had risk similar to that of shorter exposures at closer distances. The probability of transmission confirmed by a reported positive test increased initially linearly with duration of exposure (1.1% per hour) and continued increasing over several days. Whereas most exposures were short (median 0.7 h, interquartile range 0.4-1.6), transmissions typically resulted from exposures lasting between 1 h and several days (median 6 h, interquartile range 1.4-28). Households accounted for about 6% of contacts but 40% of transmissions. With sufficient preparation, privacy-preserving yet precise analyses of risk that would inform public health measures, based on digital contact tracing, could be performed within weeks of the emergence of a new pathogen.

The timing of SARS-CoV-2 transmission is a critical factor to understand the epidemic trajectory and the impact of isolation, contact tracing and other non-pharmaceutical interventions on the spread of COVID-19 epidemics. We examined the distribution of transmission events with respect to exposure and onset of symptoms. We show that for symptomatic individuals, the timing of transmission of SARS-CoV-2 is more strongly linked to the onset of clinical symptoms of COVID-19 than to the time since infection. We found that it was approximately centered and symmetric around the onset of symptoms, with three quarters of events occurring in the window from 2-3 days before to 2-3 days after. However, we caution against overinterpretation of the right tail of the distribution, due to its dependence on behavioural factors and interventions. We also found that the pre-symptomatic infectious period extended further back in time for individuals with longer incubation periods. This strongly suggests that information about when a case was infected should be collected where possible, in order to assess how far into the past their contacts should be traced. Overall, the fraction of transmission from strictly pre-symptomatic infections was high (41%; 95%CI 31-50%), which limits the efficacy of symptom-based interventions, and the large fraction of transmissions (35%; 95%CI 26-45%) that occur on the same day or the day after onset of symptoms underlines the critical importance of individuals distancing themselves from others as soon as they notice any symptoms, even if they are mild. Rapid or at-home testing and contextual risk information would greatly facilitate efficient early isolation.

Mobile phone apps implementing algorithmic contact tracing can speed up the process of tracing newly diagnosed individuals, spreading information instantaneously back through a past contact network to inform them that they are at risk of being infected, and thus allow them to take appropriate social distancing and testing measures. The aim of non-pharmaceutical infection prevention is to move a population towards herd protection, a state where a population maintains R​ 0 <​1, thus making it impossible for a pathogen to cause an epidemic. Here, we address epidemiological issues that affect the feasibility of an algorithmic approach to instantaneous contact tracing; ethical and implementation issues are addressed separately. First we quantify the parameters of COVID-19 in a framework that is consistent with the renewal equation formulation of epidemic spread. Second, we use an analytical solution to application of first-degree contact tracing in the renewal equation model to explore combinations of efficacy that can induce herd protection (R​ 0 <​1). With the emergence of the novel viral pathogen SARS-CoV-2, of clear potential for a global pandemic with high fatality rates and incapacitated health systems, the question of prevention has critical priority. We come to the conclusion that isolating symptomatic cases and tracing their contacts in a classical manner is not sufficiently fast to stop the spread of the epidemic and needs to be accompanied by measures of social distancing that are disruptive to a wide number of people. We show that first-degree instantaneous contact tracing, informing users when they can move safely or when to seek medical help and avoid vulnerable individuals, has the potential to stop the spread of the epidemic if used by a sufficiently large number of people with reasonable fidelity.

In May 2020 the UK introduced a Test, Trace, Isolate programme in response to the COVID-19 pandemic. The programme was first rolled out on the Isle of Wight and included Version 1 of the NHS contact tracing app. We used COVID-19 daily case data to infer incidence of new infections and estimate the reproduction number R for each of 150 Upper Tier Local Authorities in England, and at the National level, before and after the launch of the programme on the Isle of Wight. We used Bayesian and Maximum-Likelihood methods to estimate R, and compared the Isle of Wight to other areas using a synthetic control method. We observed significant decreases in incidence and R on the Isle of Wight immediately after the launch. These results are robust across each of our approaches. Our results show that the sub-epidemic on the Isle of Wight was controlled significantly more effectively than the sub-epidemics of most other Upper Tier Local Authorities, changing from having the third highest reproduction number R (of 150) before the intervention to the tenth lowest afterwards. The data is not yet available to establish a causal link. However, the findings highlight the need for further research to determine the causes of this reduction, as these might translate into local and national non-pharmaceutical intervention strategies in the period before a treatment or vaccination becomes available.

Background: Phylogenetic reconstruction is a necessary first step in many analyses which use whole genome sequence data from bacterial populations. There are many available methods to infer phylogenies, and these have various advantages and disadvantages, but few unbiased comparisons of the range of approaches have been made. Methods: We simulated data from a defined “true tree” using a realistic evolutionary model. We built phylogenies from this data using a range of methods, and compared reconstructed trees to the true tree using two measures, noting the computational time needed for different phylogenetic reconstructions. We also used real data from Streptococcus pneumoniae alignments to compare individual core gene trees to a core genome tree. Results: We found that, as expected, maximum likelihood trees from good quality alignments were the most accurate, but also the most computationally intensive. Using less accurate phylogenetic reconstruction methods, we were able to obtain results of comparable accuracy; we found that approximate results can rapidly be obtained using genetic distance based methods. In real data we found that highly conserved core genes, such as those involved in translation, gave an inaccurate tree topology, whereas genes involved in recombination events gave inaccurate branch lengths. We also show a tree-of-trees, relating the results of different phylogenetic reconstructions to each other. Conclusions: We recommend three approaches, depending on requirements for accuracy and computational time. Quicker approaches that do not perform full maximum likelihood optimisation may be useful for many analyses requiring a phylogeny, as generating a high quality input alignment is likely to be the major limiting factor of accurate tree topology. We have publicly released our simulated data and code to enable further comparisons.

Reconstructing who infected whom is a central challenge in analysing epidemiological data. Recently, advances in sequencing technology have led to increasing interest in Bayesian approaches to inferring who infected whom using genetic data from pathogens. The logic behind such approaches is that isolates that are nearly genetically identical are more likely to have been recently transmitted than those that are very different. A number of methods have been developed to perform this inference. However, testing their convergence, examining posterior sets of transmission trees and comparing methods' performance are challenged by the fact that the object of inference - the transmission tree - is a complicated discrete structure. We introduce a metric on transmission trees to quantify distances between them. The metric can accommodate trees with unsampled individuals, and highlights differences in the source case and in the number of infections per infector. We illustrate its performance on simple simulated scenarios and on posterior transmission trees from a TB outbreak. We find that the metric reveals where the posterior is sensitive to the priors, and where collections of trees are composed of distinct clusters. We use the metric to define median trees summarising these clusters. Quantitative tools to compare transmission trees to each other will be required for assessing MCMC convergence, exploring posterior trees and benchmarking diverse methods as this field continues to mature.

Viral phylogenetic methods contribute to understanding how HIV spreads in populations, and thereby help guide the design of prevention interventions. So far, most analyses have been applied to well-sampled concentrated HIV-1 epidemics in wealthy countries. To direct the use of phylogenetic tools to where the impact of HIV-1 is greatest, the Phylogenetics And Networks for Generalized HIV Epidemics in Africa (PANGEA-HIV) consortium generates full-genome viral sequences from across sub-Saharan Africa. Analyzing these data presents new challenges, since epidemics are principally driven by heterosexual transmission and a smaller fraction of cases is sampled. Here, we show that viral phylogenetic tools can be adapted and used to estimate epidemiological quantities of central importance to HIV-1 prevention in sub-Saharan Africa. We used a community-wide methods comparison exercise on simulated data, where participants were blinded to the true dynamics they were inferring. Two distinct simulations captured generalized HIV-1 epidemics, before and after a large community-level intervention that reduced infection levels. Five research groups participated. Structured coalescent modeling approaches were most successful: phylogenetic estimates of HIV-1 incidence, incidence reductions, and the proportion of transmissions from individuals in their first 3 months of infection correlated with the true values (Pearson correlation > 90%), with small bias. However, on some simulations, true values were markedly outside reported confidence or credibility intervals. The blinded comparison revealed current limits and strengths in using HIV phylogenetics in challenging settings, provided benchmarks for futuremethods' development, and supports using the latest generation of phylogenetic tools to advance HIV surveillance and prevention.

Background Multidrug-resistant tuberculosis poses a major threat to the success of tuberculosis control programs worldwide. Understanding how drug-resistant tuberculosis evolves can inform the development of new therapeutic and preventive strategies. Methods Here, we use novel genome-wide analysis techniques to identify polymorphisms that are associated with drug resistance, adaptive evolution and the structure of the phylogenetic tree. A total of 471 samples from different patients collected between 2009 and 2013 in the Lima suburbs of Callao and Lima South were sequenced on the Illumina MiSeq platform with 150bp paired-end reads. After alignment to the reference H37Rv genome, variants were called using standardized methodology. Genome-wide analysis was undertaken using custom written scripts implemented in R software. Results High quality homoplastic single nucleotide polymorphisms were observed in genes known to confer drug resistance as well as genes in the Mycobacterium tuberculosis ESX secreted protein pathway, pks12, and close to toxin/anti-toxin pairs. Correlation of homoplastic variant sites identified that many were significantly correlated, suggestive of epistasis. Variation in genes coding for ESX secreted proteins also significantly disrupted phylogenetic structure. Mutations in ESX genes in key antigenic epitope positions were also found to disrupt tree topology. Conclusion Variation in these genes have a biologically plausible effect on immunogenicity and virulence. This makes functional characterization warranted to determine the effects of these polymorphisms on bacterial fitness and transmission.

The increasing availability of large genomic data sets as well as the advent of Bayesian phylogenetics facilitates the investigation of phylogenetic incongruence, which can result in the impossibility of representing phylogenetic relationships using a single tree. While sometimes considered as a nuisance, phylogenetic incongruence can also reflect meaningful biological processes as well as relevant statistical uncertainty, both of which can yield valuable insights in evolutionary studies. We introduce a new tool for investigating phylogenetic incongruence through the exploration of phylogenetic tree landscapes. Our approach, implemented in the R package treespace, combines tree metrics and multivariate analysis to provide low-dimensional representations of the topological variability in a set of trees, which can be used for identifying clusters of similar trees and group-specific consensus phylogenies. treespace also provides a user-friendly web interface for interactive data analysis and is integrated alongside existing standards for phylogenetics. It fills a gap in the current phylogenetics toolbox in R and will facilitate the investigation of phylogenetic results.

Evolutionary relationships are described by phylogenetic trees, but a central barrier in many fields is the difficulty of interpreting data containing conflicting phylogenetic signals. Obtaining credible trees that capture the relationships present in complex data is one of the fundamental challenges in evolution today. We present a way to map trees which extracts distinct alternative evolutionary relationships embedded in data and resolves phylogenetic uncertainty. Our method reveals a remarkably distinct phylogenetic signature in the VP30 gene of Ebolavirus, indicating possible recombination with significant implications for vaccine development. Moving to higher organisms, we use our approach to detect alternative histories of the evolution of anole lizards. Our approach has the capacity to resolve key areas of uncertainty in the study of evolution, and to broaden the credibility and appeal of phylogenetic methods.

Viral phylogenetic methods contribute to understanding how HIV spreads in populations, and thereby help guide the design of prevention interventions. So far, most analyses have been applied to well-sampled concentrated HIV-1 epidemics in wealthy countries. To direct the use of phylogenetic tools to where the impact of HIV-1 is greatest, the Phylogenetics And Networks for Generalized HIV Epidemics in Africa (PANGEA-HIV) consortium generates full-genome viral sequences from across sub-Saharan Africa. Analyzing these data presents new challenges, since epidemics are principally driven by heterosexual transmission and a smaller fraction of cases is sampled. Here, we show that viral phylogenetic tools can be adapted and used to estimate epidemiological quantities of central importance to HIV-1 prevention in sub-Saharan Africa. We used a community-wide methods comparison exercise on simulated data, where participants were blinded to the true dynamics they were inferring. Two distinct simulations captured generalized HIV-1 epidemics, before and after a large community-level intervention that reduced infection levels. Five research groups participated. Structured coalescent modeling approaches were most successful: phylogenetic estimates of HIV-1 incidence, incidence reductions, and the proportion of transmissions from individuals in their first 3 months of infection correlated with the true values (Pearson correlation> 90%), with small bias. However, on some simulations, true values were markedly outside reported confidence or credibility intervals. The blinded comparison revealed current limits and strengths in using HIV phylogenetics in challenging settings, provided benchmarks for future methods’ development, and supports using the latest generation of phylogenetic tools to advance HIV surveillance and prevention.

Key predistribution schemes for resource-constrained networks are methods for allocating symmetric keys to devices in such a way as to provide an efficient trade-off between key storage, connectivity and resilience. While there have been many suggested constructions for key predistribution schemes, a general understanding of the design principles on which to base such constructions is somewhat lacking. Indeed even the tools from which to develop such an understanding are currently limited, which results in many relatively ad hoc proposals in the research literature. It has been suggested that a large edge-expansion coefficient in the key graph is desirable for efficient key predistribution schemes. However, attempts to create key predistribution schemes from known expander graph constructions have only provided an extreme in the trade-off between connectivity and resilience: namely, they provide perfect resilience at the expense of substantially lower connectivity than can be achieved with the same key storage. Our contribution is twofold. First, we prove that many existing key predistribution schemes produce key graphs with good expansion. This provides further support and justification for their use, and confirms the validity of expansion as a sound design principle. Second, we propose the use of incidence graphs and concurrence graphs as tools to represent, design and analyse key predistribution schemes. We show that these tools can lead to helpful insights and new constructions.

We present a formalisation of a category of schemes that we refer to as broadcast-enhanced key predistribution schemes (BEKPSs). These schemes are suitable for networks with access to a trusted base station and an authenticated broadcast channel. We demonstrate that the access to these extra resources allows for the creation of BEKPSs with advantages over key predistribution schemes such as flexibility and more efficient revocation. There are many possible ways to implement BEKPSs, and we propose a framework for describing and analysing them. In their paper “From Key Predistribution to Key Redistribution,” Cichoń et al. [2010] propose a scheme for “redistributing” keys to a wireless sensor network using a broadcast channel after an initial key predistribution. We classify this as a BEKPS and analyse it in that context. We provide simpler proofs of some results from their paper, give a precise analysis of the resilience of their scheme, and discuss possible modifications. We then study two scenarios where BEKPSs may be particularly desirable and propose a suitable family of BEKPSs for each case. We demonstrate that they are practical and efficient to implement, and our analysis shows their effectiveness in achieving suitable trade-offs between the conflicting priorities in resource-constrained networks.

Providing security for a wireless sensor network composed of small sensor nodes with limited battery power and memory can be a non-trivial task. A variety of key predistribution schemes have been proposed which allocate symmetric keys to the sensor nodes before deployment. In this paper we examine the role of expander graphs in key predistribution schemes for wireless sensor networks. Roughly speaking, a graph has good expansion if every 'small' subset of vertices has a 'large' neighbourhood, and intuitively, expansion is a desirable property for graphs of networks. It has been claimed that good expansion in the product graph is necessary for 'optimal' networks. We demonstrate flaws in this claim, argue instead that good expansion is desirable in the intersection graph, and discuss how this can be achieved. We then consider key predistribution schemes based on expander graph constructions and compare them to other schemes in the literature. Finally, we propose the use of expansion and other graph-theoretical techniques as metrics for assessing key predistribution schemes and their resulting wireless sensor networks.

A commonly used metric for comparing the resilience of key predistribution schemes is fails, which measures the proportion of network connections which are ‘broken’ by an adversary which has compromised s nodes. In ‘Random key predistribution schemes for sensor networks’, Chan, Perrig and Song present a formula for measuring the resilience in a class of random key predistribution schemes called q-composite schemes. We present a correction to this formula for schemes where more than one key may be used to secure a link between a pair of nodes. Our corrected formula features an additional parameter which makes it applicable to a wider variety of random key predistribution schemes, including the original Eschenauer Gligor scheme. We also present a simplification of the formula for calculating connectivity. We refer to the recent paper by Yum and Lee which also claims to correct the original formula for the q-composite scheme. However the resulting formula is complicated, computationally demanding, and hard to understand. The formula which we propose and prove is easily computable and can be applied to a wider range of schemes.

Robert Hinch​1​, Will Probert​1​, Anel Nurtay​1​, Michelle Kendall​1​, Chris Wymant​1​, Matthew Hall​1​, Katrina Lythgoe​1​, Ana Bulas Cruz​1​, Lele Zhao​1​, Andrea Stewart​1​, Luca Ferretti​1​, Michael Parker​2​, Ares Meroueh​3​, Bryn Mathias​3​, Scott Stevenson​3​, Daniel Montero​4​, James Warren​4​, Nicole K Mather​4​, Anthony Finkelstein​5​, Lucie Abeler-Dörner​1​, David Bonsall​1​, Christophe Fraser​1