The number and pattern of viral genomic reassortments are not necessarily identifiable from segment trees.

Reassortment is an evolutionary process common in viruses with segmented genomes. These viruses can swap whole genomic segments during cellular co-infection, giving rise to novel progeny formed from the mixture of parental segments. Because large-scale genome rearrangements have the potential to generate new phenotypes, reassortment is important to both evolutionary biology and public health research. However, statistical inference of the pattern of reassortment events from phylogenetic data is exceptionally difficult, potentially involving inference of general graphs in which individual segment trees are embedded. In this paper, we argue that, in general, the number and pattern of reassortment events are not identifiable from segment trees alone, even with theoretically ideal data. We call this fact the fundamental problem of reassortment, which we illustrate using the concept of the `first-infection tree', a typically but not always counterfactual genealogy that would have been observed in the segment trees had no reassortment occurred. Further, we illustrate four additional problems that can arise logically in the inference of reassortment events and show, using simulated data, that these problems are not rare and can potentially distort our perception of reassortment even in small data sets. Finally, we discuss how existing methods can be augmented or adapted to account for not only the fundamental problem of reassortment but also the four additional situations that can complicate the inference of reassortment.

Vaccination may be economically and epidemiologically advantageous over frequent screening for gonorrhea prevention.

BACKGROUND: Gonorrhea's rapid development of antimicrobial resistance underscores the importance of new prevention modalities. Recent evidence suggests that a serogroup B meningococcal vaccine may be partially effective against gonococcal infection. However, the viability of vaccination and the role it should play in gonorrhea prevention is an open question. METHODS: We modeled the transmission of gonorrhea over a 10-year period in a heterosexual population to find optimal patterns of year-over-year investment of a fixed budget in vaccination and screening programs. Each year, resources could be allocated to vaccinating people or enrolling them in a quarterly screening program. Stratifying by mode (vaccination vs screening), sex (male vs female), and enrollment venue (background screening vs symptomatic visit) we consider eight different ways of controlling gonorrhea. We then found the year-over-year pattern of investment among those eight controls that most reduced the incidence of gonorrhea under different assumptions. A compartmental transmission model was parameterized from existing literature in the U.S. context. RESULTS: Vaccinating men with recent symptomatic infection, which selected for higher sexual activity, was optimal for population-level gonorrhea control. Given a prevention budget of $3 per capita, 9.5% of infections could be averted ($299 per infection averted), decreasing gonorrhea sequelae and associated antimicrobial use by similar percentages. These results were consistent across sensitivity analyses that increased the budget, prioritized incidence or prevalence reductions in women, or lowered screening costs. Under a scenario where only screening was implemented, just 5.5% of infections were averted. CONCLUSIONS: A currently available vaccine, though only modestly effective, may be superior to frequent testing for population-level gonorrhea control.

Inferring Viral Transmission Time from Phylogenies for Known Transmission Pairs.

When the time of an HIV transmission event is unknown, methods to identify it from virus genetic data can reveal the circumstances that enable transmission. We developed a single-parameter Markov model to infer transmission time from an HIV phylogeny constructed of multiple virus sequences from people in a transmission pair. Our method finds the statistical support for transmission occurring in different possible time slices. We compared our time-slice model results to previously described methods: a tree-based logical transmission interval, a simple parsimony-like rules-based method, and a more complex coalescent model. Across simulations with multiple transmitted lineages, different transmission times relative to the source's infection, and different sampling times relative to transmission, we found that overall our time-slice model provided accurate and narrower estimates of the time of transmission. We also identified situations when transmission time or direction was difficult to estimate by any method, particularly when transmission occurred long after the source was infected and when sampling occurred long after transmission. Applying our model to real HIV transmission pairs showed some agreement with facts known from the case investigations. We also found, however, that uncertainty on the inferred transmission time was driven more by uncertainty from time calibration of the phylogeny than from the model inference itself. Encouragingly, comparable performance of the Markov time-slice model and the coalescent model-which make use of different information within a tree-suggests that a new method remains to be described that will make full use of the topology and node times for improved transmission time inference.

Modeling the evolution of segment trees reveals deficiencies in current inferential methods for genomic reassortment.

Reassortment is an evolutionary process common in viruses with segmented genomes. These viruses can swap whole genomic segments during cellular co-infection, giving rise to new viral variants. Large-scale genome rearrangements, such as reassortment, have the potential to quickly generate new phenotypes, making the understanding of viral reassortment important to both evolutionary biology and public health research. In this paper, we argue that reassortment cannot be reliably inferred from incongruities between segment phylogenies using the established remove-and-rejoin or coalescent approaches. We instead show that reassortment must be considered in the context of a broader population process that includes the dynamics of the infected hosts. Using illustrative examples and simulation we identify four types of evolutionary events that are difficult or impossible to reconstruct with incongruence-based methods. Further, we show that these specific situations are very common and will likely occur even in small samples. Finally, we argue that existing methods can be augmented or modified to account for all the problematic situations that we identify in this paper. Robust assessment of the role of reassortment in viral evolution is difficult, and we hope to provide conceptual clarity on some important methodological issues that can arise in the development of the next generation of tools for studying reassortment.

Inferring viral transmission time from phylogenies for known transmission pairs.

When the time of an HIV transmission event is unknown, methods to identify it from virus genetic data can reveal the circumstances that enable transmission. We developed a single-parameter Markov model to infer transmission time from an HIV phylogeny constructed of multiple virus sequences from people in a transmission pair. Our method finds the statistical support for transmission occurring in different possible time slices. We compared our time-slice model results to previously-described methods: a tree-based logical transmission interval, a simple parsimony-like rules-based method, and a more complex coalescent model. Across simulations with multiple transmitted lineages, different transmission times relative to the source's infection, and different sampling times relative to transmission, we found that overall our time-slice model provided accurate and narrower estimates of the time of transmission. We also identified situations when transmission time or direction was difficult to estimate by any method, particularly when transmission occurred long after the source was infected and when sampling occurred long after transmission. Applying our model to real HIV transmission pairs showed some agreement with facts known from the case investigations. We also found, however, that uncertainty on the inferred transmission time was driven more by uncertainty from time-calibration of the phylogeny than from the model inference itself. Encouragingly, comparable performance of the Markov time-slice model and the coalescent model-which make use of different information within a tree-suggests that a new method remains to be described that will make full use of the topology and node times for improved transmission time inference.

Swift and extensive Omicron outbreak in China after sudden exit from 'zero-COVID' policy.

In late 2022, China transitioned from a strict 'zero-COVID' policy to rapidly abandoning nearly all interventions and data reporting. This raised great concern about the presumably-rapid but unreported spread of the SARS-CoV-2 Omicron variant in a very large population of very low pre-existing immunity. By modeling a combination of case count and survey data, we show that Omicron spread extremely rapidly, at a rate of 0.42/day (95% credibility interval: [0.35, 0.51]/day), translating to an epidemic doubling time of 1.6 days ([1.6, 2.0] days) after the full exit from zero-COVID on Dec. 7, 2022. Consequently, we estimate that the vast majority of the population (97% [95%, 99%], sensitivity analysis lower limit of 90%) was infected during December, with the nation-wide epidemic peaking on Dec. 23. Overall, our results highlight the extremely high transmissibility of the variant and the importance of proper design of intervention exit strategies to avoid large infection waves.

Estimating the strength of selection for new SARS-CoV-2 variants.

Controlling the SARS-CoV-2 pandemic becomes increasingly challenging as the virus adapts to human hosts through the continual emergence of more transmissible variants. Simply observing that a variant is increasing in frequency is relatively straightforward, but more sophisticated methodology is needed to determine whether a new variant is a global threat and the magnitude of its selective advantage. We present two models for quantifying the strength of selection for new and emerging variants of SARS-CoV-2 relative to the background of contemporaneous variants. These methods range from a detailed model of dynamics within one country to a broad analysis across all countries, and they include alternative explanations such as migration and drift. We find evidence for strong selection favoring the D614G spike mutation and B.1.1.7 (Alpha), weaker selection favoring B.1.351 (Beta), and no advantage of R.1 after it spreads beyond Japan. Cutting back data to earlier time horizons reveals that uncertainty is large very soon after emergence, but that estimates of selection stabilize after several weeks. Our results also show substantial heterogeneity among countries, demonstrating the need for a truly global perspective on the molecular epidemiology of SARS-CoV-2.

Different evolutionary pathways of HIV-1 between fetus and mother perinatal transmission pairs indicate unique immune selection in fetuses.

Study of evolution and selection pressure on HIV-1 in fetuses will lead to a better understanding of the role of immune responses in shaping virus evolution and vertical transmission. Detailed genetic analyses of HIV-1 env gene from 12 in utero transmission pairs show that most infections (67%) occur within 2 months of childbirth. In addition, the env sequences from long-term-infected fetuses are highly divergent and form separate phylogenetic lineages from their cognate maternal viruses. Host-selection sites unique to neonate viruses are identified in regions frequently targeted by neutralizing antibodies and T cell immune responses. Identification of unique selection sites in the env gene of fetal viruses indicates that the immune system in fetuses is capable of exerting selection pressure on viral evolution. Studying selection and evolution of HIV-1 or other viruses in fetuses can be an alternative approach to investigate adaptive immunity in fetuses.

Estimating the strength of selection for new SARS-CoV-2 variants.

Controlling the SARS-CoV-2 pandemic becomes increasingly challenging as the virus adapts to human hosts through the continual emergence of more transmissible variants. Simply observing that a variant is increasing in frequency is relatively straightforward, but more sophisticated methodology is needed to determine whether a new variant is a global threat and the magnitude of its selective advantage. We present three methods for quantifying the strength of selection for new and emerging variants of SARS-CoV-2 relative to the background of contemporaneous variants. These methods range from a detailed model of dynamics within one country to a broad analysis across all countries, and they include alternative explanations such as migration and drift. We find evidence for strong selection favoring the D614G spike mutation and B.1.1.7 (Alpha), weaker selection favoring B.1.351 (Beta), and no advantage of R.1 after it spreads beyond Japan. Cutting back data to earlier time horizons reveals large uncertainty very soon after emergence, but that estimates of selection stabilize after several weeks. Our results also show substantial heterogeneity among countries, demonstrating the need for a truly global perspective on the molecular epidemiology of SARS-CoV-2.

Within-Host Phenotypic Evolution and the Population-Level Control of Chronic Viral Infections by Treatment and Prophylaxis.

Chronic viral infections can persist for decades spanning thousands of viral generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose an expandable mathematical framework for understanding how the emergence of genetic and phenotypic diversity affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. Our frameworks allows both neutral and phenotypic evolution, and we consider the specific evolution of contagiousness, resistance to therapy, and efficacy of prophylaxis. We compute both the controlled and uncontrolled, population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. We used these results to discuss the conditions under which the relative efficacy of prophylactic versus therapeutic methods of control are superior. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data.

Getting more from heterogeneous HIV-1 surveillance data in a high immigration country: estimation of incidence and undiagnosed population size using multiple biomarkers.

BACKGROUND: Most HIV infections originate from individuals who are undiagnosed and unaware of their infection. Estimation of this quantity from surveillance data is hard because there is incomplete knowledge about (i) the time between infection and diagnosis (TI) for the general population, and (ii) the time between immigration and diagnosis for foreign-born persons. METHODS: We developed a new statistical method for estimating the incidence of HIV-1 and the number of undiagnosed people living with HIV (PLHIV), based on dynamic modelling of heterogeneous HIV-1 surveillance data. The methods consist of a Bayesian non-linear mixed effects model using multiple biomarkers to estimate TI of HIV-1-positive individuals, and a novel incidence estimator which distinguishes between endogenous and exogenous infections by modelling explicitly the probability that a foreign-born person was infected either before or after immigration. The incidence estimator allows for direct calculation of the number of undiagnosed persons. The new methodology is illustrated combining heterogeneous surveillance data from Sweden between 2003 and 2015. RESULTS: A leave-one-out cross-validation study showed that the multiple-biomarker model was more accurate than single biomarkers (mean absolute error 1.01 vs ≥1.95). We estimate that 816 [95% credible interval (CI) 775-865] PLHIV were undiagnosed in 2015, representing a proportion of 10.8% (95% CI 10.3-11.4%) of all PLHIV. CONCLUSIONS: The proposed methodology will enhance the utility of standard surveillance data streams and will be useful to monitor progress towards and compliance with the 90-90-90 UNAIDS target.

Systematic evaluation of the population-level effects of alternative treatment strategies on the basic reproduction number.

An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R0, is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a number of different treatment strategies on the basic reproduction number. All our results are valid for sufficiently small values of the control. However, in many cases it is possible to extend this analysis to larger values of the control as was illustrated by examples.

Assessing Uncertainty in an Anatomical Site-Specific Gonorrhea Transmission Model of Men Who Have Sex With Men.

BACKGROUND: Increased gonorrhea detection highlights the need for additional prevention efforts. Gonorrhea may only be acquired when there is contact between infected and uninfected anatomical sites. With 3 sites of infection, this leads to 7 plausible routes of men who have sex with men (MSM) transmission: urethra-to-rectum, rectum-to-urethra, urethra-to-oropharynx, rectum-to-oropharynx, oropharynx-to-urethra, oropharynx-to-rectum, and oropharynx-to-oropharynx. We characterize the uncertainty and potential importance of transmission from each anatomical site using a deterministic compartmental mathematical model. METHODS: We developed a model of site-specific gonococcal infection, where individuals are infected at 0, 1, 2, or all 3 sites. Sexual behavior and infection duration parameters were fixed similar to a recent model analysis of Australian MSM. Markov chain Monte Carlo methods were used to sample the posterior distribution of transmission probabilities that were consistent with site-specific prevalence in American MSM populations under specific scenarios. Scenarios were defined by whether transmission routes may or may not transmit by constraining specific transmission probabilities to zero rather than fitting them. RESULTS: Transmission contributions from each site have greater uncertainty when more routes may transmit; in the most extreme case, when all routes may transmit, the oropharynx can contribute 0% to 100% of all transmissions. In contrast, when only anal or oral sex may transmit, transmission from the oropharynx can account for only 0% to 25% of transmission. Intervention effectiveness against transmission from each site also has greater uncertainty when more routes may transmit. CONCLUSIONS: Even under ideal conditions (ie, when site-specific gonococcal prevalence, relative rates of specific sex acts, and duration of infection at each anatomical site are known and do not vary), the relative importance of different anatomical sites for gonococcal infection transmission cannot be inferred with precision. Additional data informing per act transmissibility are needed to understand site-specific gonococcal infection transmission. This understanding is essential for predicting population-specific intervention effectiveness.

Accidental Father-to-Son HIV-1 Transmission During the Seroconversion Period.

A 4-year-old child born to an HIV-1 seronegative mother was diagnosed with HIV-1, the main risk factor being transmission from the child's father who was seroconverting at the time of the child's birth. In the context of a forensic investigation, we aimed to identify the source of infection of the child and date of the transmission event. Samples were collected from the father and child at two time points about 4 years after the child's birth. Partial segments of three HIV-1 genes (gag, pol, and env) were sequenced and maximum likelihood (ML) and Bayesian methods were used to determine direction and estimate date of transmission. Neutralizing antibodies were determined using a single cycle assay. Bayesian trees displayed a paraphyletic-monophyletic topology in all three genomic regions, with the father's host label at the root, which is consistent with father-to-son transmission. ML trees found similar topologies in gag and pol and a monophyletic-monophyletic topology in env. Analysis of the time of the most recent common ancestor of each HIV-1 gene population indicated that the child was infected shortly after the father. Consistent with the infection history, both father and son developed broad and potent HIV-specific neutralizing antibody responses. In conclusion, the direction of transmission implicated the father as the source of transmission. Transmission occurred during the seroconversion period when the father was unaware of the infection and was likely accidental. This case shows how genetic, phylogenetic, and serological data can contribute for the forensic investigation of HIV transmission.

Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series.

Mathematical models play a central role in epidemiology. For example, models unify heterogeneous data into a single framework, suggest experimental designs, and generate hypotheses. Traditional methods based on deterministic assumptions, such as ordinary differential equations (ODE), have been successful in those scenarios. However, noise caused by random variations rather than true differences is an intrinsic feature of the cellular/molecular/social world. Time series data from patients (in the case of clinical science) or number of infections (in the case of epidemics) can vary due to both intrinsic differences or incidental fluctuations. The use of traditional fitting methods for ODEs applied to noisy problems implies that deviation from some trend can only be due to error or parametric heterogeneity, that is noise can be wrongly classified as parametric heterogeneity. This leads to unstable predictions and potentially misguided policies or research programs. In this paper, we quantify the ability of ODEs under different hypotheses (fixed or random effects) to capture individual differences in the underlying data. We explore a simple (exactly solvable) example displaying an initial exponential growth by comparing state-of-the-art stochastic fitting and traditional least squares approximations. We also provide a potential approach for determining the limitations and risks of traditional fitting methodologies. Finally, we discuss the implications of our results for the interpretation of data from the 2014-2015 Ebola epidemic in Africa.

Numerical optimal control for HIV prevention with dynamic budget allocation.

This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant results.

Donor-Recipient Identification in Para- and Poly-phyletic Trees Under Alternative HIV-1 Transmission Hypotheses Using Approximate Bayesian Computation.

Diversity of the founding population of Human Immunodeficiency Virus Type 1 (HIV-1) transmissions raises many important biological, clinical, and epidemiological issues. In up to 40% of sexual infections, there is clear evidence for multiple founding variants, which can influence the efficacy of putative prevention methods, and the reconstruction of epidemiologic histories. To infer who-infected-whom, and to compute the probability of alternative transmission scenarios while explicitly taking phylogenetic uncertainty into account, we created an approximate Bayesian computation (ABC) method based on a set of statistics measuring phylogenetic topology, branch lengths, and genetic diversity. We applied our method to a suspected heterosexual transmission case involving three individuals, showing a complex monophyletic-paraphyletic-polyphyletic phylogenetic topology. We detected that seven phylogenetic lineages had been transmitted between two of the individuals based on the available samples, implying that many more unsampled lineages had also been transmitted. Testing whether the lineages had been transmitted at one time or over some length of time suggested that an ongoing superinfection process over several years was most likely. While one individual was found unlinked to the other two, surprisingly, when evaluating two competing epidemiological priors, the donor of the two that did infect each other was not identified by the host root-label, and was also not the primary suspect in that transmission. This highlights that it is important to take epidemiological information into account when analyzing support for one transmission hypothesis over another, as results may be nonintuitive and sensitive to details about sampling dates relative to possible infection dates. Our study provides a formal inference framework to include information on infection and sampling times, and to investigate ancestral node-label states, transmission direction, transmitted genetic diversity, and frequency of transmission.

Phylogenetically resolving epidemiologic linkage.

Although the use of phylogenetic trees in epidemiological investigations has become commonplace, their epidemiological interpretation has not been systematically evaluated. Here, we use an HIV-1 within-host coalescent model to probabilistically evaluate transmission histories of two epidemiologically linked hosts. Previous critique of phylogenetic reconstruction has claimed that direction of transmission is difficult to infer, and that the existence of unsampled intermediary links or common sources can never be excluded. The phylogenetic relationship between the HIV populations of epidemiologically linked hosts can be classified into six types of trees, based on cladistic relationships and whether the reconstruction is consistent with the true transmission history or not. We show that the direction of transmission and whether unsampled intermediary links or common sources existed make very different predictions about expected phylogenetic relationships: (i) Direction of transmission can often be established when paraphyly exists, (ii) intermediary links can be excluded when multiple lineages were transmitted, and (iii) when the sampled individuals' HIV populations both are monophyletic a common source was likely the origin. Inconsistent results, suggesting the wrong transmission direction, were generally rare. In addition, the expected tree topology also depends on the number of transmitted lineages, the sample size, the time of the sample relative to transmission, and how fast the diversity increases after infection. Typically, 20 or more sequences per subject give robust results. We confirm our theoretical evaluations with analyses of real transmission histories and discuss how our findings should aid in interpreting phylogenetic results.

Recombination Enhances HIV-1 Envelope Diversity by Facilitating the Survival of Latent Genomic Fragments in the Plasma Virus Population.

HIV-1 is subject to immune pressure exerted by the host, giving variants that escape the immune response an advantage. Virus released from activated latent cells competes against variants that have continually evolved and adapted to host immune pressure. Nevertheless, there is increasing evidence that virus displaying a signal of latency survives in patient plasma despite having reduced fitness due to long-term immune memory. We investigated the survival of virus with latent envelope genomic fragments by simulating within-host HIV-1 sequence evolution and the cycling of viral lineages in and out of the latent reservoir. Our model incorporates a detailed mutation process including nucleotide substitution, recombination, latent reservoir dynamics, diversifying selection pressure driven by the immune response, and purifying selection pressure asserted by deleterious mutations. We evaluated the ability of our model to capture sequence evolution in vivo by comparing our simulated sequences to HIV-1 envelope sequence data from 16 HIV-infected untreated patients. Empirical sequence divergence and diversity measures were qualitatively and quantitatively similar to those of our simulated HIV-1 populations, suggesting that our model invokes realistic trends of HIV-1 genetic evolution. Moreover, reconstructed phylogenies of simulated and patient HIV-1 populations showed similar topological structures. Our simulation results suggest that recombination is a key mechanism facilitating the persistence of virus with latent envelope genomic fragments in the productively infected cell population. Recombination increased the survival probability of latent virus forms approximately 13-fold. Prevalence of virus with latent fragments in productively infected cells was observed in only 2% of simulations when we ignored recombination, while the proportion increased to 27% of simulations when we allowed recombination. We also found that the selection pressures exerted by different fitness landscapes influenced the shape of phylogenies, diversity trends, and survival of virus with latent genomic fragments. Our model predicts that the persistence of latent genomic fragments from multiple different ancestral origins increases sequence diversity in plasma for reasonable fitness landscapes.

HIV-1 transmission during early infection in men who have sex with men: a phylodynamic analysis.

BACKGROUND: Conventional epidemiological surveillance of infectious diseases is focused on characterization of incident infections and estimation of the number of prevalent infections. Advances in methods for the analysis of the population-level genetic variation of viruses can potentially provide information about donors, not just recipients, of infection. Genetic sequences from many viruses are increasingly abundant, especially HIV, which is routinely sequenced for surveillance of drug resistance mutations. We conducted a phylodynamic analysis of HIV genetic sequence data and surveillance data from a US population of men who have sex with men (MSM) and estimated incidence and transmission rates by stage of infection. METHODS AND FINDINGS: We analyzed 662 HIV-1 subtype B sequences collected between October 14, 2004, and February 24, 2012, from MSM in the Detroit metropolitan area, Michigan. These sequences were cross-referenced with a database of 30,200 patients diagnosed with HIV infection in the state of Michigan, which includes clinical information that is informative about the recency of infection at the time of diagnosis. These data were analyzed using recently developed population genetic methods that have enabled the estimation of transmission rates from the population-level genetic diversity of the virus. We found that genetic data are highly informative about HIV donors in ways that standard surveillance data are not. Genetic data are especially informative about the stage of infection of donors at the point of transmission. We estimate that 44.7% (95% CI, 42.2%-46.4%) of transmissions occur during the first year of infection. CONCLUSIONS: In this study, almost half of transmissions occurred within the first year of HIV infection in MSM. Our conclusions may be sensitive to un-modeled intra-host evolutionary dynamics, un-modeled sexual risk behavior, and uncertainty in the stage of infected hosts at the time of sampling. The intensity of transmission during early infection may have significance for public health interventions based on early treatment of newly diagnosed individuals.