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SARS-CoV-2 epidemiology and evolution

Goal: Studying the spread and the evolution of SARS-CoV-2 at the within- and between-host levels using various type of data (incidence, sequences, Ct).

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Phylodynamic analyses generate important and timely data to optimise public health response to SARS-CoV-2 outbreaks and epidemics. However, their implementation is hampered by the massive amount of sequence data and the difficulty to parameterise dedicated software packages. We introduce the COVFlow pipeline, accessible at https://gitlab.in2p3.fr/ete/CoV-flow, which allows a user to select sequences from the Global Initiative on Sharing Avian Influenza Data (GISAID) database according to user-specified criteria, to perform basic phylogenetic analyses, and to produce an XML file to be run in the Beast2 software package. We illustrate the potential of this tool by studying two sets of sequences from the Delta variant in two French regions. This pipeline can facilitate the use of virus sequence data at the local level, for instance, to track the dynamics of a particular lineage or variant in a region of interest.
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Immune waning is key to the timely anticipation of COVID-19 long-term dynamics. We assess the impact of periodic vaccination campaigns using a compartmental epidemiological model with multiple age structures and parameterised using empiric time-dependent vaccine protection data. Despite the uncertainty inherent to such scenarios, we show that vaccination campaigns decreases the yearly number of COVID-19 admissions. However, especially if restricted to individuals over 60 years old, vaccination on its own seems insufficient to prevent thousands of hospital admissions and it suffers the comparison with non-pharmaceutical interventions aimed at decreasing infection transmission. The combination of such interventions and vaccination campaigns appear to provide the greatest reduction in hospital admissions.
We analyzed 324,734 SARS-CoV-2 variant screening tests from France enriched with 16,973 whole-genome sequences sampled during September 1, 2021-February 28, 2022. Results showed the estimated growth advantage of the Omicron variant over the Delta variant to be 105% (95% CI 96%-114%) and that of the BA.2 lineage over the BA.1 lineage to be 49% (95% CI 44%-52%). Quantitative PCR cycle threshold values were consistent with an increased ability of Omicron to generate breakthrough infections. Epidemiologic modeling shows that, in spite of its decreased virulence, the Omicron variant can generate important critical COVID-19 activity in hospitals in France. The magnitude of the BA.2 wave in hospitals depends on the level of relaxing of control measures but remains lower than that of BA.1 in median scenarios.
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Since early 2021, SARS‐CoV‐2 variants of concern (VOCs) have been causing epidemic rebounds in many countries. Their properties are well characterised at the epidemiological level but the potential underlying within‐host determinants remain poorly understood. We analyse a longitudinal cohort of 6,944 individuals with 14,304 cycle threshold (Ct) values of RT‐qPCR VOC screening tests performed in the general population and hospitals in France between February 6 and August 21, 2021. To convert Ct values into numbers of virus copies, we performed an additional analysis using droplet digital PCR (ddPCR). We find that the number of viral genome copies reaches a higher peak value and has a slower decay rate in infections caused by Alpha variant compared to that caused by historical lineages. Following the evidence that viral genome copies in upper respiratory tract swabs are informative on contagiousness, we show that the kinetics of the Alpha variant translate into significantly higher transmission potentials, especially in older populations. Finally, comparing infections caused by the Alpha and Delta variants, we find no significant difference in the peak viral copy number. These results highlight that some of the differences between variants may be detected in virus load variations. This article is protected by copyright. All rights reserved.
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Background The COVID-19 pandemic has led to an unprecedented daily use of RT-PCR tests. These tests are interpreted qualitatively for diagnosis, and the relevance of the test result intensity, i.e. the number of quantification cycles (Cq), is debated because of strong potential biases. Aim We explored the possibility to use Cq values from SARS-CoV-2 screening tests to better understand the spread of an epidemic and to better understand the biology of the infection. Methods We used linear regression models to analyse a large database of 793,479 Cq values from tests performed on more than 2 million samples between 21 January and 30 November 2020, i.e. the first two pandemic waves. We performed time series analysis using autoregressive integrated moving average (ARIMA) models to estimate whether Cq data information improves short-term predictions of epidemiological dynamics. Results Although we found that the Cq values varied depending on the testing laboratory or the assay used, we detected strong significant trends associated with patient age, number of days after symptoms onset or the state of the epidemic (the temporal reproduction number) at the time of the test. Furthermore, knowing the quartiles of the Cq distribution greatly reduced the error in predicting the temporal reproduction number of the COVID-19 epidemic. Conclusion Our results suggest that Cq values of screening tests performed in the general population generate testable hypotheses and help improve short-term predictions for epidemic surveillance.
The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. A global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.
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We analysed 131,478 SARS-CoV-2 variant screening tests performed in France from September 1st to December 18, 2021. Tests consistent with the presence of the Omicron variant exhibit significantly higher cycle threshold Ct values, which could indicate lower amounts of virus genetic material. We estimate that the transmission advantage of the Omicron variant over the Delta variant is +105% (95% confidence interval: 96-114%). Based on these data, we use mechanistic mathematical modelling to explore scenarios for early 2022.
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Estimating the date at which an epidemic started in a country and the date at which it can end depending on interventions intensity are important to guide public health responses. Both are potentially shaped by similar factors including stochasticity (due to small population sizes), superspreading events, and memory effects (the fact that the occurrence of some events, e.g. recovering from an infection, depend on the past, e.g. the number of days since the infection). Focusing on COVID-19 epidemics, we develop and analyse mathematical models to explore how these three factors may affect early and final epidemic dynamics. Regarding the date of origin, we find limited effects on the mean estimates, but strong effects on their variances. Regarding the date of extinction following lockdown onset, mean values decrease with stochasticity or with the presence of superspreading events. These results underline the importance of accounting for heterogeneity in infection history and transmission patterns to accurately capture early and late epidemic dynamics.
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France was one of the first countries to be reached by the COVID-19 pandemic. Here, we analyse 196 SARS-Cov-2 genomes collected between Jan 24 and Mar 24 2020, and perform a phylodynamics analysis. In particular, we analyse the doubling time, reproduction number (Rt) and infection duration associated with the epidemic wave that was detected in incidence data starting from Feb 27. Different models suggest a slowing down of the epidemic in Mar, which would be consistent with the implementation of the national lock-down on Mar 17. The inferred distributions for the effective infection duration and Rt are in line with those estimated from contact tracing data. Finally, based on the available sequence data, we estimate that the French epidemic wave originated between mid-Jan and early Feb. Overall, this analysis shows the potential to use sequence genomic data to inform public health decisions in an epidemic crisis context and calls for further analyses with denser sampling.
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Simulating nationwide realistic individual movements with a detailed geographical structure can help optimize public health policies. However, existing tools have limited resolution or can only account for a limited number of agents. We introduce Epidemap, a new framework that can capture the daily movement of more than 60 million people in a country at a building-level resolution in a realistic and computationally efficient way. By applying it to the case of an infectious disease spreading in France, we uncover hitherto neglected effects, such as the emergence of two distinct peaks in the daily number of cases or the importance of local density in the timing of arrival of the epidemic. Finally, we show that the importance of super-spreading events strongly varies over time.
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The Covid-19 pandemic outbreak was followed by an huge amount of modeling studies in order to rapidly gain insights to implement the best public health policies. However, most of those compartmental models used a classical ordinary differential equations (ODEs) system based formalism that came with the tacit assumption the time spent in each compartment does not depend of the time already spent in it. To overcome this "memoryless" issue, a widely used workaround is to artificially increase and chain the number of compartments of an unique reality (e.g. many compartments for infected individuals). It allows for a greater heterogeneity and thus be closer to the observed situation, at the cost of rendering the whole model more difficult to apprehend and parametrize. We propose here an alternative formalism based on a partial differential equations (PDEs) system instead of ordinary differential equations, which provides naturally a memory structure for each compartment, and thus allows to keep a restrained number of compartments. We use such a model applied to the French situation, accounting for vaccinal and natural immunity. The results seem to indicate that the vaccination rate is not enough to ensure the end of the epidemic, but, above all, highlight a huge uncertainty attributable to the age-structured contact matrix.
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SARS-CoV-2 variants raise concern regarding the mortality caused by COVID-19 epidemics. We analyse 88,375 cycle amplification (Ct) values from variant-specific RT-PCR tests performed between January 26 and March 13, 2021. We estimate that on March 12, nearly 85% of the infections were caused by the Alpha variant and that its transmission advantage over wild type strains was between 38 and 44%. We also find that tests positive for Alpha and Beta/Gamma variants exhibit significantly lower cycle threshold (Ct) values.
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Analysing 92,598 variant screening tests performed on SARS-CoV-2 positive samples collected in France between 1 July and 31 August 2021 shows an increase of Kappa-like infections. Full genome sequencing reveals that these correspond to Delta variants bearing the S:E484Q mutation. Most of these sequences belong to a phylogenetic cluster and also bear the S:T95I mutation. Further monitoring is needed to determine if this trend is driven by undocumented superspreading events or an early signal of future viral evolutionary dynamics
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Ct values are commonly used as proxies of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) 'viral load'. Since coronaviruses are positive single-stranded RNA [(+)ssRNA] viruses, current reverse transcription (RT)-qPCR target amplification does not distinguish replicative from transcriptional RNA. Although analyses of Ct values remain informative, equating them with viral load may lead to flawed conclusions as it is presently unknown whether (and to what extent) variation in Ct reflects variation in viral load or in gene expression.
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The effectiveness of individual prophylaxis of symptomatic or severe COVID-19 by anti-SARS-CoV-2 vaccination is now well established. However, real-life quantification of the vaccine impact on critical COVID-19 forms -- which require critical care and may lead to death -- is still lacking, especially because simultaneous reduction in community spread has to be accounted for. In this study, we use an epidemiological model tailored to capture hospital dynamics in France to investigate counterfactual scenarios, including purely collective and purely individual vaccines. The model estimates the transmissibility reduction from breakthrough infections to 43% ([32 -- 55]% 95%-likelihood interval) and that 39,100 critical care stays ([26,100 -- 57,100] 95% confidence interval) and 47,400 ([36,200-62,800]) hospital deaths have been prevented by the French vaccination campaign by August 20 2021 -- respectively corresponding to 46% and 57% relative preventions of these outcomes. Furthermore, we show that most of the critical COVID-19 forms have been prevented by the collective component of the vaccine rather than individual prophylaxis, despite its greater effectiveness. These results are in line with the accelerating decrease in fatality ratio with vaccine coverage we highlight in worldwide data.
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Forecasting SARS-CoV-2 epidemic trends with confidence more than a few weeks ahead is almost impossible as these entirely depend on political decisions. We address this problem by investigating the consequences for the health system of an epidemic wave of a given size. This approach yields semi-quantitative results that depend on the proportion of the population already infected and vaccinated. We introduce the COVimpact software, which allows users to visualise estimated numbers of ICU admissions, deaths, and infections stratified by age class at the French departmental, regional, or national level caused by the wave. We illustrate the usefulness of our approach by showing that for France, even with a 95% vaccination coverage, the current vaccine efficiency against the delta variant would make a large epidemic wave infecting 25% of the population difficult to sustain for the current hospital bed occupancy capacity. Overall, using the final epidemic wave size and ignoring detailed epidemiological dynamics yields valuable and practical insights to optimise public health response to epidemics.
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Background Coronavirus disease (COVID-19) was detected in Wuhan, China in 2019 and spread worldwide within few weeks. The COVID-19 epidemic started to gain traction in France in March 2020. Sub-national hospital admissions and deaths were then recorded daily and served as the main policy indicators. Concurrently, mobile phone positioning data have been curated to determine the frequency of users being colocalized within a given distance. Contrarily to individual tracking data, these can provide a proxy of human contact networks between subnational administrative units. Methods Motivated by numerous studies correlating human mobility data and disease incidence, we developed predictive time series models of hospital incidence between July 2020 and April 2021. We added human contact network analytics such as clustering coefficients, contact network strength, null links or curvature as regressors. FindingsWe found that predictions can be improved substantially (more than 50%) both at the national and sub-national for up to two weeks. Our sub-national analysis also revealed the importance of spatial structure, as incidence in colocalized administrative units improved predictions. This original application of network analytics from co-localisation data to epidemic spread opens new perspectives for epidemics forecasting and public health.
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We analysed 9,030 variant-specific RT-PCR tests performed on SARS-CoV-2-positive samples collected in France between 31 May and 21 June 2021. This analysis revealed rapid growth of the Delta variant in three of the 13 metropolitan French regions and estimated a +79% (95% confidence interval: 52–110%) transmission advantage compared with the Alpha variant. The next weeks will prove decisive and the magnitude of the estimated transmission advantages of the Delta variant could represent a major challenge for public health authorities.
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The COVID-19 pandemic has led to a resurgence of the debate on whether host-parasite interactions should evolve towards avirulence. In this review, we first show that SARS-CoV-2 virulence is evolving, before explaining why some expect the mortality caused by the epidemic to converge to wards that of human seasonal alphacoronaviruses. Leaning on existing theory, we then include viral evolution into the picture and discuss hypotheses explaining why the virulence has increased since the beginning of the pandemic. Finally, we mention some potential scenarios for the future.
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Coronavirus disease (COVID-19) was detected in Wuhan, China in 2019 and spread worldwide within few weeks. The COVID-19 epidemic started to gain traction in France in March 2020. Sub-national hospital admissions and deaths were then recorded daily and served as the main policy indicators. Concurrently, mobile phone positioning data have been curated to determine the frequency of users being colocalized within a given distance. Contrarily to individual tracking data, these can provide a proxy of human contact networks between subnational administrative units. Motivated by numerous studies correlating human mobility data and disease incidence, we developed predictive time series models of hospital incidence between July 2020 and April 2021. Adding human contact network analytics such as clustering coefficients, contact network strength, null links or curvature as regressors, we found that predictions can be improved substantially (more than 50%) both at the national and sub-national for up to two weeks. Our sub-national analysis also revealed the importance of spatial structure, as incidence in colocalized administrative units improved predictions. This original application of network analytics from co-localisation data to epidemic spread opens new perspectives for epidemics forecasting and public health.
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Background The COVID-19 epidemic has spread rapidly within aged-care facilities (ACFs), where the infection-fatality ratio is high. It is therefore urgent to evaluate the efficiency of infection prevention and control (IPC) measures in reducing SARS-CoV-2 transmission. Methods We analysed the COVID-19 outbreaks that took place between March and May 2020 in 12 ACFs using reverse transcription–polymerase chain reaction (RT–PCR) and serological tests for SARS-CoV-2 infection. Using maximum-likelihood approaches and generalized linear mixed models, we analysed the proportion of infected residents in ACFs and identified covariates associated with the proportion of infected residents. Results The secondary-attack risk was estimated at 4.1%, suggesting a high efficiency of the IPC measures implemented in the region. Mask wearing and the establishment of COVID-19 zones for infected residents were the two main covariates associated with lower secondary-attack risks. Conclusions Wearing masks and isolating potentially infected residents appear to be associated with a more limited spread of SARS-CoV-2 in ACFs.
Analysing 5,061 variant-specific tests performed on SARS-CoV-2 positive samples collected in France between 31 May and 8 June 2021 reveals a rapid growth of the δ variant in the Ile-de-France region. The next weeks will prove decisive but the magnitude of the estimated transmission advantage (with a 95% confidence interval between 67 and 120\%) could represent a major challenge for public health authorities.
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To assess SARS-CoV-2 variants spread, we analysed 36,590 variant-specific reverse-transcription-PCR tests performed on samples from 12 April–7 May 2021 in France. In this period, contrarily to January–March 2021, variants of concern (VOC) β (B.1.351 lineage) and/or γ (P.1 lineage) had a significant transmission advantage over VOC α (B.1.1.7 lineage) in Île-de-France (15.8%; 95% confidence interval (CI): 15.5–16.2) and Hauts-de-France (17.3%; 95% CI: 15.9–18.7) regions. This is consistent with VOC β’s immune evasion abilities and high proportions of prior-SARS-CoV-2-infected persons in these regions.
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SARS-CoV-2 variants are causing epidemic rebounds in many countries. By analyzing longitudinal cycle threshold (Ct) values from screening tests in the general population and hospitals, we find that infections caused by variant lineages have higher peak viral load than wild type lineages and, for the B.1.1.7 lineage, have a longer infectious period duration. Linking within-host kinetics to transmission data suggests that infections caused by variants have higher transmission potentials and that their epidemiological fitness may depend on the demography of the host population.
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SARS-CoV-2 variants threaten our ability to control COVID-19 epidemics. We analyzed 36,590 variant-specific RT-PCR tests performed on samples collected between April 12 and May 7, 2021 in France to compare variant spread. Contrarily to January to March 2021, we found that the V2 variant had a significant transmission advantage over V1 in some regions (15.1 to 16.1% in Ile-de-France and 16.1 to 18.8% in Hauts-de-France). This shift in transmission advantage is consistent with the immune evasion abilities of V2 and the high levels of immunization in these regions.
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SARS-CoV-2 virus has spread over the world rapidly creating one of the largest pandemics ever. The absence of immunity, presymptomatic transmission, and the relatively high level of virulence of the COVID-19 infection led to a massive flow of patients in intensive care units (ICU). This unprecedented situation calls for rapid and accurate mathematical models to best inform public health policies. We develop an original parsimonious discrete-time model that accounts for the effect of the age of infection on the natural history of the disease. Analysing the ongoing COVID-19 in France as a test case, through the publicly available time series of nationwide hospital mortality and ICU activity, we estimate the value of the key epidemiological parameters and the impact of lock-down implementation delay. This work shows that including memory-effects in the modelling of COVID-19 spreading greatly improves the accuracy of the fit to the epidemiological data. We estimate that the epidemic wave in France started on Jan 20 [Jan 12, Jan 28] (95% likelihood interval) with a reproduction number initially equal to 2.99 [2.59, 3.39], which was reduced by the national lock-down started on Mar 17 to 24 [21, 27] of its value. We also estimate that the implementation of the latter a week earlier or later would have lead to a difference of about respectively -13k and +50k hospital deaths by the end of lock-down. The present parsimonious discrete-time framework constitutes a useful tool for now- and forecasting simultaneously community incidence and ICU capacity strain.
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In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.
Several recent studies used results of SARS-CoV-2 RT-qPCR, Ct (threshold cycle), as proxies of viral load1. Unfortunately, an important aspect of this virus’ biology is neglected: Coronaviruses being (+)ssRNA viruses the form of RNA they use for replication is identical to the form used for transcription. It is therefore not obvious which process, replication or transcription, is quantified by RT-qPCR. To make matters more complicated, Coronaviruses produce several kinds of mRNA, genomic (= full size) and subgenomic (carrying only some genes), hence modulating their gene expression1. As shown by Finkel et al. the different mRNAs of SARS-CoV-2 occur at different densities in cell cultures. Because of their location on the viral genome the different targets of RT-qPCR are differentially affected, some being carried by more types of mRNA than others. Further, gene expression being affected by environmental and genetic factors, the quantity of RNA revealed by RT-qPCR may consequently vary due to differences in replication rates, in expression rates, or in both. It is thus unclear how good a proxy of viral load Ct values are, or what differences in Ct values may reflect.Even though the process underlying them is poorly characterized, and despite additional known biases in sample quality and RT-PCR protocols, quantitative analyses of Ct may nevertheless be highly informative e.g. in allowing to detect patterns in ‘levels of RNA’ in patients with different properties (gender, age, severe vs. mild disease, stage of infection) or in allowing to relate these patterns to epidemic properties in populations. For example, given that a priori replication levels should be the same for all genes of these monopartite viruses, differences in Ct among markers lying in different viral genes for should reflect different expression profiles. Such observations could thus help reveal interesting, and potentially epidemiologically significant, variations e.g. among SARS-CoV-2 variants.
The SARS-CoV-2 pandemic has led to an unprecedented daily use of molecular RT-PCR tests. These tests are interpreted qualitatively for diagnosis, and the relevance of the test result intensity, i.e. the number of amplification cycles (Ct), is debated because of strong potential biases. We analyze a national database of tests performed on more than 2 million individuals between January and November 2020. Although we find Ct values to vary depending on the testing laboratory or the assay used, we detect strong significant trends with patient age, number of days after symptoms onset, or the state of the epidemic (the temporal reproduction number) at the time of the test. These results suggest that Ct values can be used to improve short-term predictions for epidemic surveillance.
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SARS-CoV-2 variants raise major concerns regarding the control of COVID-19 epidemics. We analyse 40,000 specific RT-PCR tests performed on SARS-CoV-2-positive samples collected between Jan 26 and Feb 16, 2021. We find a high transmission advantage of variants and show that their spread in the country is more advanced than anticipated.
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Estimating the date at which an epidemic started in a country and the date at which it can end depending on interventions intensity are important to guide public health responses. Both are potentially shaped by similar factors including stochasticity (due to small population sizes), superspreading events, and memory effects. Focusing on COVID-19 epidemics, we develop and analyse mathematical models to explore how these three factors may affect early and final epidemic dynamics. Regarding the date of origin, we find limited effects on the mean estimates, but strong effects on their variances. Regarding the date of extinction following lock-down onset, mean values decrease with stochasticity or with the presence of superspreading events. These results underline the importance of accounting for heterogeneity in infection history and transmission patterns to make accurate predictions regarding epidemic temporal estimates.
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Analysing the spread of COVID-19 epidemics in a timely manner is essential for public health authorities. However, raw numbers may be misleading because of spatial and temporal variations. We introduce Rt2, an R-program with a shiny interface, which uses incidence data, i.e. number of new cases per day, to compute variations in the temporal reproduction number (ℛ t ), which corresponds to the average number of secondary infections caused by an infected person. This number is computed with the R0 package, which better captures past variations, and the EpiEstim package, which provides a more accurate estimate of current values. ℛ t can be computed in different countries using either the daily number of new cases or of deaths. For France, these numbers can also be computed at the regional and departmental level using also daily numbers of hospital and ICU admissions. Finally, in addition to ℛ t , we represent the incidence using a one-week sliding window to buffer daily variations. Overall, Rt2 provides an accurate and timely overview of the state and speed of spread of COVID-19 epidemics at different scales, using different metrics.
Since Dec 2019, the COVID-19 epidemic has spread over the globe creating one of the greatest pandemics ever witnessed. This epidemic wave will only begin to roll back once a critical proportion of the population is immunised, either by mounting natural immunity following infection, or by vaccination. The latter option can minimise the cost in terms of human lives but it requires to wait until a safe and efficient vaccine is developed, a period estimated to last at least 18 months. In this work, we use optimal control theory to explore the best strategy to implement while waiting for the vaccine. We seek a solution minimizing deaths and costs due to the implementation of the control strategy itself. We find that such a solution leads to an increasing level of control with a maximum reached near the 16th month of the epidemics and a steady decrease until vaccine deployment. The average containment level is approximately 50% during the 25-months period for vaccine deployment. This strategy strongly out-performs others with constant or cycling allocations of the same amount of resources to control the outbreak. This work opens new perspectives to mitigate the effects of the ongoing COVID-19 pandemics, and be used as a proof-of-concept in using mathematical modelling techniques to enlighten decision making and public health management in the early times of an outbreak.
In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been infected for. The latter allows to take into account the variation of infectiousness as a function of time since infection. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. social distancing) are of great importance to mitigate the pandemic. We propose a model with a double continuous structure by host age and time since infection. By applying optimal control theory to our age-structured model, we identify a solution minimizing deaths and costs associated with the implementation of the control strategy itself. This strategy depends on the age heterogeneity between individuals and consists in a relatively high isolation intensity over the older populations during a hundred days, followed by a steady decrease in a way that depends on the cost associated to a such control. The isolation of the younger population is weaker and occurs only if the cost associated with the control is relatively low. We show that the optimal control strategy strongly outperforms other strategies such as uniform constant control over the whole populations or over its younger fraction. These results bring new facts the debate about age-based control interventions and open promising avenues of research, for instance of age-based contact tracing.
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Studying the spread and the evolution of SARS-CoV-2 at the within- and between-host levels using various type of data (incidence, sequences, Ct).