Using early detection data to estimate the date of emergence of an epidemic outbreak.

While the first infection of an emerging disease is often unknown, information on early cases can be used to date it. In the context of the COVID-19 pandemic, previous studies have estimated dates of emergence (e.g., first human SARS-CoV-2 infection, emergence of the Alpha SARS-CoV-2 variant) using mainly genomic data. Another dating attempt used a stochastic population dynamics approach and the date of the first reported case. Here, we extend this approach to use a larger set of early reported cases to estimate the delay from first infection to the Nth case. We first validate our framework by running our model on simulated data. We then apply our model using data on Alpha variant infections in the UK, dating the first Alpha infection at (median) August 21, 2020 (95% interpercentile range across retained simulations (IPR): July 23-September 5, 2020). Next, we apply our model to data on COVID-19 cases with symptom onset before mid-January 2020. We date the first SARS-CoV-2 infection in Wuhan at (median) November 28, 2019 (95% IPR: November 2-December 9, 2019). Our results fall within ranges previously estimated by studies relying on genomic data. Our population dynamics-based modelling framework is generic and flexible, and thus can be applied to estimate the starting time of outbreaks in contexts other than COVID-19.

What we can and cannot learn from SARS-CoV-2 and animals in metagenomic samples from the Huanan market.

While the exact context of the emergence of SARS-CoV-2 remains uncertain, data accumulated since 2020 have provided an increasingly more precise picture of Wuhan's Huanan Seafood Wholesale Market, to which the earliest clusters of human cases of Covid-19 were linked. After the market closed on January 1st 2020, teams from the Chinese Center for Disease Control and Prevention collected environmental samples, and sequenced them. Metagenomic sequencing data from these samples were shared in early 2023. These data confirmed that non-human animals susceptible to SARS-CoV-2 were present in the market before it closed, but also that these animals were located in the side of the market with most human cases, and in a corner with comparatively more SARS-CoV-2-positive environmental samples. The environmental samples were however collected after abundant human-to-human transmission had taken place in the market, precluding any identification of a non-human animal host. Jesse Bloom recently investigated associations between SARS-CoV-2 and non-human animals, concluding that the data failed to indicate whether non-human animals were infected by SARS-CoV-2, despite this being an already acknowledged limitation of the data. Here I explain why a correlation analysis could not confidently conclude which hosts(s) may have shed SARS-CoV-2 in the market, and I rebut the suggestion that such analyses had been encouraged. I show that Bloom's investigation ignores the temporal and spatial structure of the data, which led to incorrect interpretations. Finally, I show that criteria put forward by Bloom to identify the host(s) that shed environmental SARS-CoV-2 would also exclude humans. Progress on the topic of SARS-CoV-2's origin requires a clear distinction between scientific studies and news articles (mis)interpreting them.

Genetic tracing of market wildlife and viruses at the epicenter of the COVID-19 pandemic.

Zoonotic spillovers of viruses have occurred through the animal trade worldwide. The start of the COVID-19 pandemic was traced epidemiologically to the Huanan Wholesale Seafood Market, the site with the most reported wildlife vendors in the city of Wuhan, China. Here, we analyze publicly available qPCR and sequencing data from environmental samples collected in the Huanan market in early 2020. We demonstrate that the SARS-CoV-2 genetic diversity linked to this market is consistent with market emergence, and find increased SARS-CoV-2 positivity near and within a particular wildlife stall. We identify wildlife DNA in all SARS-CoV-2 positive samples from this stall. This includes species such as civets, bamboo rats, porcupines, hedgehogs, and one species, raccoon dogs, known to be capable of SARS-CoV-2 transmission. We also detect other animal viruses that infect raccoon dogs, civets, and bamboo rats. Combining metagenomic and phylogenetic approaches, we recover genotypes of market animals and compare them to those from other markets. This analysis provides the genetic basis for a short list of potential intermediate hosts of SARS-CoV-2 to prioritize for retrospective serological testing and viral sampling.

A stochastic analysis of the interplay between antibiotic dose, mode of action, and bacterial competition in the evolution of antibiotic resistance.

The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.

Pulled, pushed or failed: the demographic impact of a gene drive can change the nature of its spatial spread.

Understanding the temporal spread of gene drive alleles-alleles that bias their own transmission-through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing the interplay between demographic and allelic dynamics, in a one-dimensional spatial context. We focused on the traveling wave solutions, and more specifically, on the speed of gene drive invasion (if successful). We considered various timings of gene conversion (in the zygote or in the germline) and different probabilities of gene conversion (instead of assuming 100[Formula: see text] conversion as done in a previous work). We compared the types of propagation when the intrinsic growth rate of the population takes extreme values, either very large or very low. When it is infinitely large, the wave can be either successful or not, and, if successful, it can be either pulled or pushed, in agreement with previous studies (extended here to the case of partial conversion). In contrast, it cannot be pushed when the intrinsic growth rate is vanishing. In this case, analytical results are obtained through an insightful connection with an epidemiological SI model. We conducted extensive numerical simulations to bridge the gap between the two regimes of large and low growth rate. We conjecture that, if it is pulled in the two extreme regimes, then the wave is always pulled, and the wave speed is independent of the growth rate. This occurs for instance when the fitness cost is small enough, or when there is stable coexistence of the drive and the wild-type in the population after successful drive invasion. Our model helps delineate the conditions under which demographic dynamics can affect the spread of a gene drive.

Temporal, age, and geographical variation in vaccine efficacy against infection by the Delta and Omicron variants in the community in France, December 2021 to March 2022.

OBJECTIVES: We aimed to quantify how the vaccine efficacy of BNT162b2, messenger RNA-1273, AD26.COV2-S, and ChAdOx1 nCoV-19 against detected infection by the SARS-CoV-2 Delta and Omicron variants varied by time since the last dose, vaccine scheme, age, and geographic areas. METHODS: We analyzed 3,261,749 community polymerase chain reaction tests conducted by private laboratories in France from December 2021 to March 2022 with a test-negative design comparing vaccinated to unvaccinated individuals. RESULTS: Efficacy against detected infection by Delta was 89% (95% confidence interval, 86-91%) at 2 weeks, down to 59% (56-61%) at 26 weeks and more after the second dose. Efficacy against Omicron was 48% (45-51%) at 2 weeks, down to 4% (2-5%) at 16 weeks after the second dose. A third dose temporarily restored efficacy. Efficacy against Omicron was lower in children and the elderly. Geographical variability in efficacy may reflect variability in the ratio of the number of contacts of vaccinated vs unvaccinated individuals. This ratio ranged from 0 to +50% across departments and correlated with the number of restaurants and bars per inhabitant (beta = 15.0 [0.75-29], P-value = 0.04), places that only vaccinated individuals could access in the study period. CONCLUSION: SARS-CoV-2 vaccines conferred low and transient protection against Omicron infection.

The French Covid-19 vaccination policy did not solve vaccination inequities: a nationwide study on 64.5 million people.

BACKGROUND: To encourage Covid-19 vaccination, France introduced during the Summer 2021 a 'Sanitary Pass', which morphed into a 'Vaccine Pass' in early 2022. While the sanitary pass led to an increase in Covid-19 vaccination rates, spatial heterogeneities in vaccination rates remained. To identify potential determinants of these heterogeneities and evaluate the French sanitary and vaccine passes' efficacies in reducing them, we used a data-driven approach on exhaustive nationwide data, gathering 141 socio-economic, political and geographic indicators. METHODS: We considered the association between vaccination rates and each indicator at different time points: before the sanitary pass announcement (week 2021-W27), before the sanitary pass came into force (week 2021-W31) and 1 month after (week 2021-W35) and the equivalent dates for the vaccine pass (weeks 2021-W49, 2022-W03 and 2022-W07). RESULTS: The indicators most associated with vaccination rates were the share of local income coming from unemployment benefits, overcrowded households rate, immigrants rate and vote for an 'anti-establishment' candidate at the 2017 Presidential election. These associations increase over time. Consequently, living in a district below the median of such indicator decreases the probability to be vaccinated by about 30% at the end of the studied period, and this probability gradually decreases by deciles of these indicators. CONCLUSIONS: Our analysis reveals that factors related to poverty, immigration and trust in the government are strong determinants of vaccination rate, and that vaccination inequities tended to increase after the introduction of the French sanitary and vaccination passes.

Selection for infectivity profiles in slow and fast epidemics, and the rise of SARS-CoV-2 variants.

Evaluating the characteristics of emerging SARS-CoV-2 variants of concern is essential to inform pandemic risk assessment. A variant may grow faster if it produces a larger number of secondary infections ("R advantage") or if the timing of secondary infections (generation time) is better. So far, assessments have largely focused on deriving the R advantage assuming the generation time was unchanged. Yet, knowledge of both is needed to anticipate the impact. Here, we develop an analytical framework to investigate the contribution of both the R advantage and generation time to the growth advantage of a variant. It is known that selection on a variant with larger R increases with levels of transmission in the community. We additionally show that variants conferring earlier transmission are more strongly favored when the historical strains have fast epidemic growth, while variants conferring later transmission are more strongly favored when historical strains have slow or negative growth. We develop these conceptual insights into a new statistical framework to infer both the R advantage and generation time of a variant. On simulated data, our framework correctly estimates both parameters when it covers time periods characterized by different epidemiological contexts. Applied to data for the Alpha and Delta variants in England and in Europe, we find that Alpha confers a+54% [95% CI, 45-63%] R advantage compared to previous strains, and Delta +140% [98-182%] compared to Alpha, and mean generation times are similar to historical strains for both variants. This work helps interpret variant frequency dynamics and will strengthen risk assessment for future variants of concern.

Mutations in genes of the SARS-CoV-2 virus have generated new variants of concern, like Alpha, Delta, and more recently Omicron. These strains contain genetic modifications that help the virus spread more easily as well as altering the severity of the illness it causes. This has led to rising numbers of infections, known as epidemic waves, in many parts of the world. Tracking new variants of concern is crucial to protecting the public. To do this, scientists monitor how many people one person with the virus can infect, also known as the number of secondary infections. They may also measure when in the course of the illness an individual may pass along the virus to others. Together, these metrics help determine how fast and large an outbreak caused by a new variant will grow. The more people the new variant infects and the quicker it spreads, the more likely it is to replace existing strains of the virus. So far, most studies have assumed that the growth rate of a new variant solely depends on the number of secondary infections, and the timing of secondary infections is often not considered. To address this, Blanquart et al. built a mathematical model that combines both these parameters to determine the growth rate of new viral strains. The model showed that variants which rapidly cause secondary infections have a larger growth advantage over existing strains when the virus is more easily transmitted between individuals and the epidemic spreads rapidly. But when there is less transmission and the epidemic is declining, variants that generate secondary infections after a longer time have an advantage. For example, when control measures like mask wearing or social distancing are in place, delayed secondary infections may be more advantageous. Blanquart et al. then applied their model to data from the Alpha and Delta variant outbreaks in the United Kingdom. They found that Alpha and Delta did not change the timing of secondary infections compared to previously circulating strains. But the Alpha variant had a 54% transmission advantage over previous strains and the Delta variant had a 140% transmission advantage over Alpha. Taken together, these findings suggest that the timing of secondary infections and transmission rates both play an important role in how quickly a virus spreads. The new mathematical model created by Blanquart et al. may help epidemiologists better predict the trajectory of new SARS-CoV-2 variants and determine how to best control their spread.

Demographic feedbacks can hamper the spatial spread of a gene drive.

This paper is concerned with a reaction-diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. While previous reaction-diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure. Our findings can be extended to other bistable systems, such as the spread of cytoplasmic incompatibilities caused by Wolbachia.

The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection.

Emerging epidemics and local infection clusters are initially prone to stochastic effects that can substantially impact the early epidemic trajectory. While numerous studies are devoted to the deterministic regime of an established epidemic, mathematical descriptions of the initial phase of epidemic growth are comparatively rarer. Here, we review existing mathematical results on the size of the epidemic over time, and derive new results to elucidate the early dynamics of an infection cluster started by a single infected individual. We show that the initial growth of epidemics that eventually take off is accelerated by stochasticity. As an application, we compute the distribution of the first detection time of an infected individual in an infection cluster depending on testing effort, and estimate that the SARS-CoV-2 variant of concern Alpha detected in September 2020 first appeared in the UK early August 2020. We also compute a minimal testing frequency to detect clusters before they exceed a given threshold size. These results improve our theoretical understanding of early epidemics and will be useful for the study and control of local infectious disease clusters.

Characterisation of vaccine breakthrough infections of SARS-CoV-2 Delta and Alpha variants and within-host viral load dynamics in the community, France, June to July 2021.

We compared PCR results from SARS-CoV-2-positive patients tested in the community in France from 14 June to 30 July 2021. In asymptomatic individuals, Cq values were significantly higher in fully vaccinated than non-fully vaccinated individuals (effect size: 1.7; 95% CI: 1-2.3; p < 10-6). In symptomatic individuals and controlling for time since symptoms, the difference vanished (p = 0.26). Infections with the Delta variant had lower Cq values at symptom onset than with Alpha (effect size: -3.32; 95% CI: -4.38 to -2.25; p < 10-6).

The Effect of Habitat Choice on Evolutionary Rescue in Subdivided Populations.

AbstractEvolutionary rescue is the process by which a population, in response to an environmental change, successfully avoids extinction through adaptation. In spatially structured environments, dispersal can affect the probability of rescue. Here, we model an environment consisting of patches that degrade one after another, and we investigate the probability of rescue by a mutant adapted to the degraded habitat. We focus on the effects of dispersal and of immigration biases. We identify up to three regions delimiting the effect of dispersal on the probability of evolutionary rescue: (i) starting from low dispersal rates, the probability of rescue increases with dispersal; (ii) at intermediate dispersal rates, it decreases; and (iii) at large dispersal rates, it increases again with dispersal, except if mutants are too counterselected in not-yet-degraded patches. The probability of rescue is generally highest when mutant and wild-type individuals preferentially immigrate into patches that have already undergone environmental change. Additionally, we find that mutants that will eventually rescue the population most likely first appear in nondegraded patches. Overall, our results show that habitat choice, compared with the often-studied unbiased immigration scheme, can substantially alter the dynamics of population survival and adaptation to new environments.

Success of prophylactic antiviral therapy for SARS-CoV-2: Predicted critical efficacies and impact of different drug-specific mechanisms of action.

Repurposed drugs that are safe and immediately available constitute a first line of defense against new viral infections. Despite limited antiviral activity against SARS-CoV-2, several drugs are being tested as medication or as prophylaxis to prevent infection. Using a stochastic model of early phase infection, we evaluate the success of prophylactic treatment with different drug types to prevent viral infection. We find that there exists a critical efficacy that a treatment must reach in order to block viral establishment. Treatment by a combination of drugs reduces the critical efficacy, most effectively by the combination of a drug blocking viral entry into cells and a drug increasing viral clearance. Below the critical efficacy, the risk of infection can nonetheless be reduced. Drugs blocking viral entry into cells or enhancing viral clearance reduce the risk of infection more than drugs that reduce viral production in infected cells. The larger the initial inoculum of infectious virus, the less likely is prevention of an infection. In our model, we find that as long as the viral inoculum is smaller than 10 infectious virus particles, viral infection can be prevented almost certainly with drugs of 90% efficacy (or more). Even when a viral infection cannot be prevented, antivirals delay the time to detectable viral loads. The largest delay of viral infection is achieved by drugs reducing viral production in infected cells. A delay of virus infection flattens the within-host viral dynamic curve, possibly reducing transmission and symptom severity. Thus, antiviral prophylaxis, even with reduced efficacy, could be efficiently used to prevent or alleviate infection in people at high risk.

MetaPopGen 2.0: A multilocus genetic simulator to model populations of large size.

Multilocus genetic processes in subdivided populations can be complex and difficult to interpret using theoretical population genetics models. Genetic simulators offer a valid alternative to study multilocus genetic processes in arbitrarily complex scenarios. However, the use of forward-in-time simulators in realistic scenarios involving high numbers of individuals distributed in multiple local populations is limited by computation time and memory requirements. These limitations increase with the number of simulated individuals. We developed a genetic simulator, MetaPopGen 2.0, to model multilocus population genetic processes in subdivided populations of arbitrarily large size. It allows for spatial and temporal variation in demographic parameters, age structure, adult and propagule dispersal, variable mutation rates and selection on survival and fecundity. We developed MetaPopGen 2.0 in the R environment to facilitate its use by non-modeler ecologists and evolutionary biologists. We illustrate the capabilities of MetaPopGen 2.0 for studying adaptation to water salinity in the striped red mullet Mullus surmuletus.

Can a Population Targeted by a CRISPR-Based Homing Gene Drive Be Rescued?

CRISPR-based homing gene drive is a genetic control technique aiming to modify or eradicate natural populations. This technique is based on the release of individuals carrying an engineered piece of DNA that can be preferentially inherited by the progeny. The development of countermeasures is important to control the spread of gene drives, should they result in unanticipated damages. One proposed countermeasure is the introduction of individuals carrying a brake construct that targets and inactivates the drive allele but leaves the wild-type allele unaffected. Here we develop models to investigate the efficiency of such brakes. We consider a variable population size and use a combination of analytical and numerical methods to determine the conditions where a brake can prevent the extinction of a population targeted by an eradication drive. We find that a brake is not guaranteed to prevent eradication and that characteristics of both the brake and the drive affect the likelihood of recovering the wild-type population. In particular, brakes that restore fitness are more efficient than brakes that do not. Our model also indicates that threshold-dependent drives (drives that can spread only when introduced above a threshold) are more amenable to control with a brake than drives that can spread from an arbitrary low introduction frequency (threshold-independent drives). Based on our results, we provide practical recommendations and discuss safety issues.

Catch Me If You Can: A Spatial Model for a Brake-Driven Gene Drive Reversal.

Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may, however, have to be stopped. "Antidotes" (brakes) have been suggested, but have been so far only studied in well-mixed populations. Here, we consider a reaction-diffusion system modeling the release of a gene drive (of fitness [Formula: see text]) and a brake (fitness [Formula: see text], [Formula: see text]) in a wild-type population (fitness 1). We prove that whenever the drive fitness is at most 1/2 while the brake fitness is close to 1, coextinction of the brake and the drive occurs in the long run. On the contrary, if the drive fitness is greater than 1/2, then coextinction is impossible: the drive and the brake keep spreading spatially, leaving in the invasion wake a complicated spatiotemporally heterogeneous genetic pattern. Based on numerical experiments, we argue in favor of a global coextinction conjecture provided the drive fitness is at most 1/2, irrespective of the brake fitness. The proof relies upon the study of a related predator-prey system with strong Allee effect on the prey. Our results indicate that some drives may be unstoppable and that if gene drives are ever deployed in nature, threshold drives, that only spread if introduced in high enough frequencies, should be preferred.