A fast and scalable method for inferring phylogenetic networks from trees by aligning lineage taxon strings.

The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the minimum phylogenetic network problem, in which phylogenetic trees are first inferred, and then the smallest phylogenetic network that displays all the trees is computed. The approach takes advantage of the fact that the theory of phylogenetic trees is mature, and there are excellent tools available for inferring phylogenetic trees from a large number of biomolecular sequences. A tree-child network is a phylogenetic network satisfying the condition that every nonleaf node has at least one child that is of indegree one. Here, we develop a new method that infers the minimum tree-child network by aligning lineage taxon strings in the phylogenetic trees. This algorithmic innovation enables us to get around the limitations of the existing programs for phylogenetic network inference. Our new program, named ALTS, is fast enough to infer a tree-child network with a large number of reticulations for a set of up to 50 phylogenetic trees with 50 taxa that have only trivial common clusters in about a quarter of an hour on average.

Capturing diversity: Split systems and circular approximations for conservation.

We investigated the implications of employing a circular approximation of split systems in the calculation of maximum diversity subsets of a set of taxa in a conservation biology context where diversity is measured using Split System Diversity (SSD). We conducted a comparative analysis between the maximum SSD score and the maximum SSD set(s) of size k, efficiently determined using a circular approximation, and the true results obtained through brute-force search based on the original data. Through experimentation on simulated datasets and SNP data across 50 Atlantic Salmon populations, our findings demonstrate that employing a circular approximation can lead to the generation of an incorrect max-SSD set(s). We built a graph-based split system whose circular approximation led to a max-SSD set of size k=4 that was less than the true max-SSD set by 17.6%. This discrepancy increased to 25% for k=11 when we used a hypergraph-based split system. The same comparison on the Atlantic salmon dataset revealed a mere 1% difference. However, noteworthy disparities emerged in the population composition between the two sets. These findings underscore the importance of assessing the suitability of circular approximations in conservation biology systems. Caution is advised when relying solely on circular approximations to determine sets of maximum diversity, and careful consideration of the data characteristics is crucial for accurate results in conservation biology applications.

Pneumococcal population dynamics: Investigating vaccine-induced changes through multiscale modelling.

The mechanisms behind vaccine-induced strain replacement in the pneumococcus remain poorly understood. There is emerging evidence that distinct pneumococcal lineages can co-colonise for significant time periods, and that novel recombinants can readily emerge during natural colonisation. Despite this, patterns of post-vaccine replacement are indicative of competition between specific lineages. Here, we develop a multiscale transmission model to investigate explicitly how within host dynamics shape observed ecological patterns, both pre- and post-vaccination. Our model framework explores competition between and within strains defined by distinct antigenic, metabolic and resistance profiles. We allow for strains to freely co-colonise and recombine within hosts, and consider how each of these types may contribute to a strain's overall fitness. Our results suggest that antigenic and resistance profiles are key drivers of post-vaccine success.

The role of vaccine status homophily in the COVID-19 pandemic: a cross-sectional survey with modelling.

BACKGROUND: Vaccine homophily describes non-heterogeneous vaccine uptake within contact networks. This study was performed to determine observable patterns of vaccine homophily, as well as the impact of vaccine homophily on disease transmission within and between vaccination groups under conditions of high and low vaccine efficacy. METHODS: Residents of British Columbia, Canada, aged ≥ 16 years, were recruited via online advertisements between February and March 2022, and provided information about vaccination status, perceived vaccination status of household and non-household contacts, compliance with COVID-19 prevention guidelines, and history of COVID-19. A deterministic mathematical model was used to assess transmission dynamics between vaccine status groups under conditions of high and low vaccine efficacy. RESULTS: Vaccine homophily was observed among those with 0, 2, or 3 doses of the vaccine. Greater homophily was observed among those who had more doses of the vaccine (p < 0.0001). Those with fewer vaccine doses had larger contact networks (p < 0.0001), were more likely to report prior COVID-19 (p < 0.0001), and reported lower compliance with COVID-19 prevention guidelines (p < 0.0001). Mathematical modelling showed that vaccine homophily plays a considerable role in epidemic growth under conditions of high and low vaccine efficacy. Furthermore, vaccine homophily contributes to a high force of infection among unvaccinated individuals under conditions of high vaccine efficacy, as well as to an elevated force of infection from unvaccinated to suboptimally vaccinated individuals under conditions of low vaccine efficacy. INTERPRETATION: The uneven uptake of COVID-19 vaccines and the nature of the contact network in the population play important roles in shaping COVID-19 transmission dynamics.

Analyzing Phylogenetic Trees with a Tree Lattice Coordinate System and a Graph Polynomial.

Phylogenetic trees are a central tool in many areas of life science and medicine. They demonstrate evolutionary patterns among species, genes, and patterns of ancestry among sets of individuals. The tree shapes and branch lengths of phylogenetic trees encode evolutionary and epidemiological information. To extract information from tree shapes and branch lengths, representation and comparison methods for phylogenetic trees are needed. Representing and comparing tree shapes and branch lengths of phylogenetic trees are challenging, for a tree shape is unlabeled and can be displayed in numerous different forms, and branch lengths of a tree shape are specific to edges whose positions vary with respect to the displayed forms of the tree shape. In this article, we introduce representation and comparison methods for rooted unlabeled phylogenetic trees based on a tree lattice that serves as a coordinate system for rooted binary trees with branch lengths and a graph polynomial that fully characterizes tree shapes. We show that the introduced tree representations and metrics provide distance-based likelihood-free methods for tree clustering, parameter estimation, and model selection and apply the methods to analyze phylogenies reconstructed from virus sequences. [Graph polynomial; likelihood-free inference; phylogenetics; tree lattice; tree metrics.].

COVID-19 endgame: From pandemic to endemic? Vaccination, reopening and evolution in low- and high-vaccinated populations.

COVID-19 remains a major public health concern, with large resurgences even where there has been widespread uptake of vaccines. Waning immunity and the emergence of new variants will shape the long-term burden and dynamics of COVID-19. We explore the transition to the endemic state, and the endemic incidence in British Columbia (BC), Canada and South Africa (SA), to compare low and high vaccination coverage settings with differing public health policies, using a combination of modelling approaches. We compare reopening (relaxation of public health measures) gradually and rapidly as well as at different vaccination levels. We examine how the eventual endemic state depends on the duration of immunity, the rate of importations, the efficacy of vaccines and the transmissibility. These depend on the evolution of the virus, which continues to undergo selection. Slower reopening leads to a lower peak level of incidence and fewer overall infections in the wave following reopening: as much as a 60% lower peak and a 10% lower total in some illustrative simulations; under realistic parameters, reopening when 70% of the population is vaccinated leads to a large resurgence in cases. The long-term endemic behaviour may stabilize as late as January 2023, with further waves of high incidence occurring depending on the transmissibility of the prevalent variant, duration of immunity, and antigenic drift. We find that long term endemic levels are not necessarily lower than current pandemic levels: in a population of 100,000 with representative parameter settings (Reproduction number 5, 1-year duration of immunity, vaccine efficacy at 80% and importations at 3 cases per 100K per day) there are over 100 daily incident cases in the model. Predicted prevalence at endemicity has increased more than twofold after the emergence and spread of Omicron. The consequent burden on health care systems depends on the severity of infection in immunized or previously infected individuals.

Spatial modeling of Mycobacterium tuberculosis transmission with dyadic genetic relatedness data.

Understanding factors that contribute to the increased likelihood of pathogen transmission between two individuals is important for infection control. However, analyzing measures of pathogen relatedness to estimate these associations is complicated due to correlation arising from the presence of the same individual across multiple dyadic outcomes, potential spatial correlation caused by unmeasured transmission dynamics, and the distinctive distributional characteristics of some of the outcomes. We develop two novel hierarchical Bayesian spatial methods for analyzing dyadic pathogen genetic relatedness data, in the form of patristic distances and transmission probabilities, that simultaneously address each of these complications. Using individual-level spatially correlated random effect parameters, we account for multiple sources of correlation between the outcomes as well as other important features of their distribution. Through simulation, we show the limitations of existing approaches in terms of estimating key associations of interest, and the ability of the new methodology to correct for these issues across datasets with different levels of correlation. All methods are applied to Mycobacterium tuberculosis data from the Republic of Moldova, where we identify previously unknown factors associated with disease transmission and, through analysis of the random effect parameters, key individuals, and areas with increased transmission activity. Model comparisons show the importance of the new methodology in this setting. The methods are implemented in the R package GenePair.

Effective population size in simple infectious disease models.

Almost all models used in analysis of infectious disease outbreaks contain some notion of population size, usually taken as the census population size of the community in question. In many settings, however, the census population is not equivalent to the population likely to be exposed, for example if there are population structures, outbreak controls or other heterogeneities. Although these factors may be taken into account in the model: adding compartments to a compartmental model, variable mixing rates and so on, this makes fitting more challenging, especially if the population complexities are not fully known. In this work we consider the concept of effective population size in outbreak modelling, which we define as the size of the population involved in an outbreak, as an alternative to use of more complex models. Effective population size is an important quantity in genetics for estimation of genetic diversity loss in populations, but it has not been widely applied in epidemiology. Through simulation studies and application to data from outbreaks of COVID-19 in China, we find that simple SIR models with effective population size can provide a good fit to data which are not themselves simple or SIR.

Event-specific interventions to minimize COVID-19 transmission.

COVID-19 is a global pandemic with over 25 million cases worldwide. Currently, treatments are limited, and there is no approved vaccine. Interventions such as handwashing, masks, social distancing, and "social bubbles" are used to limit community transmission, but it is challenging to choose the best interventions for a given activity. Here, we provide a quantitative framework to determine which interventions are likely to have the most impact in which settings. We introduce the concept of "event R," the expected number of new infections due to the presence of a single infectious individual at an event. We obtain a fundamental relationship between event R and four parameters: transmission intensity, duration of exposure, the proximity of individuals, and the degree of mixing. We use reports of small outbreaks to establish event R and transmission intensity in a range of settings. We identify principles that guide whether physical distancing, masks and other barriers to transmission, or social bubbles will be most effective. We outline how this information can be obtained and used to reopen economies with principled measures to reduce COVID-19 transmission.

Long-Term Persistence of Spike Protein Antibody and Predictive Modeling of Antibody Dynamics After Infection With Severe Acute Respiratory Syndrome Coronavirus 2.

BACKGROUND: Antibodies to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been shown to neutralize the virus in vitro and prevent disease in animal challenge models on reexposure. However, the current understanding of SARS-CoV-2 humoral dynamics and longevity is conflicting. METHODS: The COVID-19 Staff Testing of Antibody Responses Study (Co-Stars) prospectively enrolled 3679 healthcare workers to comprehensively characterize the kinetics of SARS-CoV-2 spike protein (S), receptor-binding domain, and nucleoprotein (N) antibodies in parallel. Participants screening seropositive had serial monthly serological testing for a maximum of 7 months with the Meso Scale Discovery Assay. Survival analysis determined the proportion of seroreversion, while 2 hierarchical gamma models predicted the upper and lower bounds of long-term antibody trajectory. RESULTS: A total of 1163 monthly samples were provided from 349 seropositive participants. At 200 days after symptoms, >95% of participants had detectable S antibodies, compared with 75% with detectable N antibodies. S antibody was predicted to remain detectable in 95% of participants until 465 days (95% confidence interval, 370-575 days) using a "continuous-decay" model and indefinitely using a "decay-to-plateau" model to account for antibody secretion by long-lived plasma cells. S-antibody titers were correlated strongly with surrogate neutralization in vitro (R2 = 0.72). N antibodies, however, decayed rapidly with a half-life of 60 days (95% confidence interval, 52-68 days). CONCLUSIONS: The Co-Stars data presented here provide evidence for long-term persistence of neutralizing S antibodies. This has important implications for the duration of functional immunity after SARS-CoV-2 infection. In contrast, the rapid decay of N antibodies must be considered in future seroprevalence studies and public health decision-making. This is the first study to establish a mathematical framework capable of predicting long-term humoral dynamics after SARS-CoV-2 infection. CLINICAL TRIALS REGISTRATION: NCT04380896.

Cov2clusters: genomic clustering of SARS-CoV-2 sequences.

BACKGROUND: The COVID-19 pandemic remains a global public health concern. Advances in sequencing technologies has allowed for high numbers of SARS-CoV-2 whole genome sequence (WGS) data and rapid sharing of sequences through global repositories to enable almost real-time genomic analysis of the pathogen. WGS data has been used previously to group genetically similar viral pathogens to reveal evidence of transmission, including methods that identify distinct clusters on a phylogenetic tree. Identifying clusters of linked cases can aid in the regional surveillance and management of the disease. In this study, we present a novel method for producing stable genomic clusters of SARS-CoV-2 cases, cov2clusters, and compare the accuracy and stability of our approach to previous methods used for phylogenetic clustering using real-world SARS-CoV-2 sequence data obtained from British Columbia, Canada. RESULTS: We found that cov2clusters produced more stable clusters than previously used phylogenetic clustering methods when adding sequence data through time, mimicking an increase in sequence data through the pandemic. Our method also showed high accuracy when predicting epidemiologically informed clusters from sequence data. CONCLUSIONS: Our new approach allows for the identification of stable clusters of SARS-CoV-2 from WGS data. Producing high-resolution SARS-CoV-2 clusters from sequence data alone can a challenge and, where possible, both genomic and epidemiological data should be used in combination.

Phylogeography and transmission of M. tuberculosis in Moldova: A prospective genomic analysis.

BACKGROUND: The incidence of multidrug-resistant tuberculosis (MDR-TB) remains critically high in countries of the former Soviet Union, where >20% of new cases and >50% of previously treated cases have resistance to rifampin and isoniazid. Transmission of resistant strains, as opposed to resistance selected through inadequate treatment of drug-susceptible tuberculosis (TB), is the main driver of incident MDR-TB in these countries. METHODS AND FINDINGS: We conducted a prospective, genomic analysis of all culture-positive TB cases diagnosed in 2018 and 2019 in the Republic of Moldova. We used phylogenetic methods to identify putative transmission clusters; spatial and demographic data were analyzed to further describe local transmission of Mycobacterium tuberculosis. Of 2,236 participants, 779 (36%) had MDR-TB, of whom 386 (50%) had never been treated previously for TB. Moreover, 92% of multidrug-resistant M. tuberculosis strains belonged to putative transmission clusters. Phylogenetic reconstruction identified 3 large clades that were comprised nearly uniformly of MDR-TB: 2 of these clades were of Beijing lineage, and 1 of Ural lineage, and each had additional distinct clade-specific second-line drug resistance mutations and geographic distributions. Spatial and temporal proximity between pairs of cases within a cluster was associated with greater genomic similarity. Our study lasted for only 2 years, a relatively short duration compared with the natural history of TB, and, thus, the ability to infer the full extent of transmission is limited. CONCLUSIONS: The MDR-TB epidemic in Moldova is associated with the local transmission of multiple M. tuberculosis strains, including distinct clades of highly drug-resistant M. tuberculosis with varying geographic distributions and drug resistance profiles. This study demonstrates the role of comprehensive genomic surveillance for understanding the transmission of M. tuberculosis and highlights the urgency of interventions to interrupt transmission of highly drug-resistant M. tuberculosis.

COVID-19 in schools: Mitigating classroom clusters in the context of variable transmission.

Widespread school closures occurred during the COVID-19 pandemic. Because closures are costly and damaging, many jurisdictions have since reopened schools with control measures in place. Early evidence indicated that schools were low risk and children were unlikely to be very infectious, but it is becoming clear that children and youth can acquire and transmit COVID-19 in school settings and that transmission clusters and outbreaks can be large. We describe the contrasting literature on school transmission, and argue that the apparent discrepancy can be reconciled by heterogeneity, or "overdispersion" in transmission, with many exposures yielding little to no risk of onward transmission, but some unfortunate exposures causing sizeable onward transmission. In addition, respiratory viral loads are as high in children and youth as in adults, pre- and asymptomatic transmission occur, and the possibility of aerosol transmission has been established. We use a stochastic individual-based model to find the implications of these combined observations for cluster sizes and control measures. We consider both individual and environment/activity contributions to the transmission rate, as both are known to contribute to variability in transmission. We find that even small heterogeneities in these contributions result in highly variable transmission cluster sizes in the classroom setting, with clusters ranging from 1 to 20 individuals in a class of 25. None of the mitigation protocols we modeled, initiated by a positive test in a symptomatic individual, are able to prevent large transmission clusters unless the transmission rate is low (in which case large clusters do not occur in any case). Among the measures we modeled, only rapid universal monitoring (for example by regular, onsite, pooled testing) accomplished this prevention. We suggest approaches and the rationale for mitigating these larger clusters, even if they are expected to be rare.

Estimation of SARS-CoV-2 antibody prevalence through serological uncertainty and daily incidence.

Serology tests for SARS-CoV-2 provide a paradigm for estimating the number of individuals who have had an infection in the past (including cases that are not detected by routine testing, which has varied over the course of the pandemic and between jurisdictions). Such estimation is challenging in cases for which we only have limited serological data and do not take into account the uncertainty of the serology test. In this work, we provide a joint Bayesian model to improve the estimation of the sero-prevalence (the proportion of the population with SARS-CoV-2 antibodies) through integrating multiple sources of data, priors on the sensitivity and specificity of the serological test, and an effective epidemiological dynamics model. We apply our model to the Greater Vancouver area, British Columbia, Canada, with data acquired during the pandemic from the end of January to May 2020. Our estimated sero-prevalence is consistent with previous literature but with a tighter credible interval.

Le dépistage sérologique du SRAS­CoV­2 permet d'estimer le nombre de personnes qui ont déjà été infectées (y compris les cas qui ne sont pas détectés au moyen de tests de dépistage réguliers, qui ont varié au cours de la pandémie et d'une province ou d'un territoire à l'autre). Une telle estimation est difficile lorsqu'il existe peu de données sérologiques et que l'incertitude du test sérologique n'est pas prise en compte. Nous proposons dans ce travail un modèle bayésien conjoint visant à améliorer l'estimation de la séroprévalence (la proportion de la population avec des anticorps SRAS­CoV­2) en intégrant de multiples sources de données, des lois a priori sur la sensibilité et la spécificité du test sérologique, et un modèle efficace des dynamiques épidémiologiques. Nous appliquons ce modèle à des données recueillies dans la région métropolitaine de Vancouver (Colombie­Britannique, Canada) pendant la pandémie de fin janvier à mai 2020. Notre estimation de la séroprévalence est cohérente avec la littérature antérieure tout en ayant un intervalle de crédibilité plus précis.

Quantifying the impact of COVID-19 control measures using a Bayesian model of physical distancing.

Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide. It is therefore urgent to estimate the impact such measures are having. We introduce a Bayesian epidemiological model in which a proportion of individuals are willing and able to participate in distancing, with the timing of distancing measures informed by survey data on attitudes to distancing and COVID-19. We fit our model to reported COVID-19 cases in British Columbia (BC), Canada, and five other jurisdictions, using an observation model that accounts for both underestimation and the delay between symptom onset and reporting. We estimated the impact that physical distancing (social distancing) has had on the contact rate and examined the projected impact of relaxing distancing measures. We found that, as of April 11 2020, distancing had a strong impact in BC, consistent with declines in reported cases and in hospitalization and intensive care unit numbers; individuals practising physical distancing experienced approximately 0.22 (0.11-0.34 90% CI [credible interval]) of their normal contact rate. The threshold above which prevalence was expected to grow was 0.55. We define the "contact ratio" to be the ratio of the estimated contact rate to the threshold rate at which cases are expected to grow; we estimated this contact ratio to be 0.40 (0.19-0.60) in BC. We developed an R package 'covidseir' to make our model available, and used it to quantify the impact of distancing in five additional jurisdictions. As of May 7, 2020, we estimated that New Zealand was well below its threshold value (contact ratio of 0.22 [0.11-0.34]), New York (0.60 [0.43-0.74]), Washington (0.84 [0.79-0.90]) and Florida (0.86 [0.76-0.96]) were progressively closer to theirs yet still below, but California (1.15 [1.07-1.23]) was above its threshold overall, with cases still rising. Accordingly, we found that BC, New Zealand, and New York may have had more room to relax distancing measures than the other jurisdictions, though this would need to be done cautiously and with total case volumes in mind. Our projections indicate that intermittent distancing measures-if sufficiently strong and robustly followed-could control COVID-19 transmission. This approach provides a useful tool for jurisdictions to monitor and assess current levels of distancing relative to their threshold, which will continue to be essential through subsequent waves of this pandemic.

Long time frames to detect the impact of changing COVID-19 measures, Canada, March to July 2020.

BackgroundMany countries have implemented population-wide interventions to control COVID-19, with varying extent and success. Many jurisdictions have moved to relax measures, while others have intensified efforts to reduce transmission.AimWe aimed to determine the time frame between a population-level change in COVID-19 measures and its impact on the number of cases.MethodsWe examined how long it takes for there to be a substantial difference between the number of cases that occur following a change in COVID-19 physical distancing measures and those that would have occurred at baseline. We then examined how long it takes to observe this difference, given delays and noise in reported cases. We used a susceptible-exposed-infectious-removed (SEIR)-type model and publicly available data from British Columbia, Canada, collected between March and July 2020.ResultsIt takes 10 days or more before we expect a substantial difference in the number of cases following a change in COVID-19 control measures, but 20-26 days to detect the impact of the change in reported data. The time frames are longer for smaller changes in control measures and are impacted by testing and reporting processes, with delays reaching ≥ 30 days.ConclusionThe time until a change in control measures has an observed impact is longer than the mean incubation period of COVID-19 and the commonly used 14-day time period. Policymakers and practitioners should consider this when assessing the impact of policy changes. Rapid, consistent and real-time COVID-19 surveillance is important to minimise these time frames.

Transmission Trees on a Known Pathogen Phylogeny: Enumeration and Sampling.

One approach to the reconstruction of infectious disease transmission trees from pathogen genomic data has been to use a phylogenetic tree, reconstructed from pathogen sequences, and annotate its internal nodes to provide a reconstruction of which host each lineage was in at each point in time. If only one pathogen lineage can be transmitted to a new host (i.e., the transmission bottleneck is complete), this corresponds to partitioning the nodes of the phylogeny into connected regions, each of which represents evolution in an individual host. These partitions define the possible transmission trees that are consistent with a given phylogenetic tree. However, the mathematical properties of the transmission trees given a phylogeny remain largely unexplored. Here, we describe a procedure to calculate the number of possible transmission trees for a given phylogeny, and we then show how to uniformly sample from these transmission trees. The procedure is outlined for situations where one sample is available from each host and trees do not have branch lengths, and we also provide extensions for incomplete sampling, multiple sampling, and the application to time trees in a situation where limits on the period during which each host could have been infected and infectious are known. The sampling algorithm is available as an R package (STraTUS).

Beyond the SNP Threshold: Identifying Outbreak Clusters Using Inferred Transmissions.

Whole-genome sequencing (WGS) is increasingly used to aid the understanding of pathogen transmission. A first step in analyzing WGS data is usually to define "transmission clusters," sets of cases that are potentially linked by direct transmission. This is often done by including two cases in the same cluster if they are separated by fewer single-nucleotide polymorphisms (SNPs) than a specified threshold. However, there is little agreement as to what an appropriate threshold should be. We propose a probabilistic alternative, suggesting that the key inferential target for transmission clusters is the number of transmissions separating cases. We characterize this by combining the number of SNP differences and the length of time over which those differences have accumulated, using information about case timing, molecular clock, and transmission processes. Our framework has the advantage of allowing for variable mutation rates across the genome and can incorporate other epidemiological data. We use two tuberculosis studies to illustrate the impact of our approach: with British Columbia data by using spatial divisions; with Republic of Moldova data by incorporating antibiotic resistance. Simulation results indicate that our transmission-based method is better in identifying direct transmissions than a SNP threshold, with dissimilarity between clusterings of on average 0.27 bits compared with 0.37 bits for the SNP-threshold method and 0.84 bits for randomly permuted data. These results show that it is likely to outperform the SNP-threshold method where clock rates are variable and sample collection times are spread out. We implement the method in the R package transcluster.

Predicting the short-term success of human influenza virus variants with machine learning.

Seasonal influenza viruses are constantly changing and produce a different set of circulating strains each season. Small genetic changes can accumulate over time and result in antigenically different viruses; this may prevent the body's immune system from recognizing those viruses. Due to rapid mutations, in particular, in the haemagglutinin (HA) gene, seasonal influenza vaccines must be updated frequently. This requires choosing strains to include in the updates to maximize the vaccines' benefits, according to estimates of which strains will be circulating in upcoming seasons. This is a challenging prediction task. In this paper, we use longitudinally sampled phylogenetic trees based on HA sequences from human influenza viruses, together with counts of epitope site polymorphisms in HA, to predict which influenza virus strains are likely to be successful. We extract small groups of taxa (subtrees) and use a suite of features of these subtrees as key inputs to the machine learning tools. Using a range of training and testing strategies, including training on H3N2 and testing on H1N1, we find that successful prediction of future expansion of small subtrees is possible from these data, with accuracies of 0.71-0.85 and a classifier 'area under the curve' 0.75-0.9.

Systematic comparison of coexistence in models of drug-sensitive and drug-resistant pathogen strains.

A number of mathematical models have recently been proposed to explain empirical trends of pathogen diversity. In particular, long-term coexistence of both drug-sensitive and drug-resistant variants of a single pathogen is something of a mystery, given that simple models of pathogens competing for the same ecological niche predict competitive exclusion, and more complex models admitting coexistence require assumptions that may not be justified. Coinfection is among the candidate mechanisms to generate coexistence, as it occurs in many pathogens and provides the opportunity for strains to interact directly. Recently, coinfection and competitive release have been described as creating a form of negative frequency-dependent selection that promotes coexistence, and a range of models containing coinfection have been proposed as having generic stable coexistence of multiple strains. This abundance of new models presents the challenge of comparison and interpretation. To this end, we describe a dimensionless quantity that can be used to compare the amount of coexistence generated by different models. We focus on models that include coinfection, although this framework could be generalized to a larger class of structured models.