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AO_SCPLOWBSTRACTC_SCPLOWNon-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, have been widely implemented during the COVID-19 pandemic. In addition to playing an important role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply and altering the strength of selection for novel variants. However, it is unclear how NPIs might affect the emergence of novel variants of concern that are able to escape pre-existing immunity (partially or fully), are more transmissible, or cause greater mortality. Here, we analyse a stochastic two-strain epidemiological model to determine how the strength of NPIs affects the emergence of variants with similar or contrasting life-history characteristics to the wildtype. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross immunity to have a greater probability of emerging at intermediate levels of NPIs. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be implementation of strong, timely NPIs. AO_SCPLOWUTHORC_SCPLOWO_SCPCAP C_SCPCAPO_SCPLOWSUMMARYC_SCPLOWDuring the COVID-19 pandemic, a wide range of non-pharmaceutical interventions, including mask wearing, quarantine, isolation, and lockdowns, have been used by governments around the world to suppress virus transmission. Although considerable efforts have been made to understand how such interventions affect transmission, much less attention has been paid to their effects on pathogen evolution. While vaccines are well-known to affect virus evolution, non-pharmaceutical interventions also influence mutation supply and the strength of selection, and hence play a key role in the emergence of novel variants. Here, we use a relatively simple mathematical model to explore how non-pharmaceutical interventions during an epidemic affect the emergence of a novel variant of a pathogen. We show that in general, it is important to implement effective transmission-reducing public health measures in a timely manner to prevent the emergence of novel variants, which may be more transmissible, more deadly, or able to escape immunity.

In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multi-scale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multi-scale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.

During the COVID-19 pandemic, human behavior change as a result of nonpharmaceutical interventions such as isolation may have induced directional selection for viral evolution. By combining previously published empirical clinical data analysis and multi-level mathematical modeling, we found that the SARS-CoV-2 variants selected for as the virus evolved from the pre-Alpha to the Delta variant had earlier and higher infectious periods but a shorter duration of infection. Selection for increased transmissibility shapes the viral load dynamics, and the isolation measure is likely to be a driver of these evolutionary transitions. In addition, we showed that a decreased incubation period and an increased proportion of asymptomatic infection were also positively selected for as SARS-CoV-2 mutated to the extent that people did not isolate. We demonstrated that the Omicron variants evolved in these ways to adapt to human behavior. The quantitative information and predictions we present here can guide future responses in the potential arms race between pandemic interventions and viral evolution.

Infectious diseases of plants present an ongoing and increasing threat to international biosecurity, with wide-ranging implications. An important challenge in plant disease management is achieving early detection of invading pathogens, which requires effective surveillance through the implementation of appropriate monitoring programmes. However, when monitoring relies on visual inspection as a means of detection, surveillance is often hindered by a long incubation period (delay from infection to symptom onset) during which plants may be infectious but not displaying visible symptoms. ‘Sentinel’ plants–alternative susceptible host species that display visible symptoms of infection more rapidly–could be introduced to at-risk populations and included in monitoring programmes to act as early warning beacons for infection. However, while sentinel hosts exhibit faster disease progression and so allow pathogens to be detected earlier, this often comes at a cost: faster disease progression typically promotes earlier onward transmission. Here, we construct a computational model of pathogen transmission to explore this trade-off and investigate how including sentinel plants in monitoring programmes could facilitate earlier detection of invasive plant pathogens. Using Xylella fastidiosa infection in Olea europaea (European olive) as a current high profile case study, for which Catharanthus roseus (Madagascan periwinkle) is a candidate sentinel host, we apply a Bayesian optimisation algorithm to determine the optimal number of sentinel hosts to introduce for a given sampling effort, as well as the optimal division of limited surveillance resources between crop and sentinel plants. Our results demonstrate that including sentinel plants in monitoring programmes can reduce the expected prevalence of infection upon outbreak detection substantially, increasing the feasibility of local outbreak containment.

Viruses evolve in infected host populations, and host population dynamics affect viral evolution. RNA viruses with a short duration of infection and a high peak viral load, such as and SARS-CoV-2, are maintained in human populations. By contrast, RNA viruses characterized by a long infection duration and a low peak viral load (e.g., borna disease virus) can be maintained in nonhuman populations, and why the persistent viruses evolved has been rarely explored. Here, using a multi-level modeling approach including both individual-level virus infection dynamics and population-scale transmission, we consider virus evolution based on the host environment, specifically, the effect of the contact history of infected hosts. We found that, with a highly dense contact history, viruses with a high virus production rate but low accuracy are likely to be optimal, resulting in a short infectious period with a high peak viral load. In contrast, with a low-density contact history, viral evolution is toward low virus production but high accuracy, resulting in long infection durations with low peak viral load. Our study sheds light on the origin of persistent viruses and why acute viral infections but not persistent virus infection tends to prevail in human society.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Robust epidemiological knowledge and predictive modelling tools are needed to address challenging objectives, such as: understanding epidemic drivers; forecasting epidemics; and prioritising control measures. Often, mul- tiple modelling approaches can be used during an epidemic to support effective decision making in a timely manner. Modelling challenges contribute to understanding the pros and cons of different approaches and to fostering technical dialogue between modellers. In this paper, we present the results of the first modelling challenge in animal health – the ASF Challenge – which focused on a synthetic epidemic of African swine fever (ASF) on an island. The modelling approaches proposed by five independent international teams were compared. We assessed their ability to predict temporal and spatial epidemic expansion at the interface between domestic pigs and wild boar, and to prioritise a limited number of alternative interventions. We also compared their qualitative and quantitative spatio-temporal predictions over the first two one-month projection phases of the challenge. Top-performing models in predicting the ASF epidemic differed according to the challenge phase, host species, and in predicting spatial or temporal dynamics. Ensemble models built using all team-predictions out- performed any individual model in at least one phase. The ASF Challenge demonstrated that accounting for the interface between livestock and wildlife is key to increasing our effectiveness in controlling emerging animal diseases, and contributed to improving the readiness of the scientific community to face future ASF epidemics. Finally, we discuss the lessons learnt from model comparison to guide decision making.

Summary statistics, often derived from simplified models of epidemic spread, inform public health policy in real time. The instantaneous reproduction number, Rt, is predominant among these statistics, measuring the average ability of an infection to multiply. However, Rt encodes no temporal information and is sensitive to modelling assumptions. Consequently, some have proposed the epidemic growth rate, rt, i.e., the rate of change of the log-transformed case incidence, as a more temporally meaningful and model-agnostic policy guide. We examine this assertion, identifying if and when estimates of rt are more informative than those of Rt. We assess their relative strengths both for learning about pathogen transmission mechanisms and for guiding public health interventions in real time.

Lay Summary: Competition often occurs among diverse parasites within a single host, but control efforts could change its strength. We examined how the interplay between competition and control could shape the evolution of parasite traits like drug resistance and disease severity.

Funding: This work was supported by the Isaac Newton Institute (EPSRC grant no. EP/R014604/1). MEK was supported by grants from The Netherlands Organisation for Health Research and Development (ZonMw), grant number 10430022010001, and grant number 91216062, and by the H2020 Project 101003480 (CORESMA). RNT was supported by the UKRI, grant number EP/V053507/1. GR was supported by Fundação para a Ciência e a Tecnologia (FCT) project reference 131_596787873. and by the VERDI project 101045989 funded by the European Union. LP and CO are funded by the Wellcome Trust and the Royal Society (grant 202562/Z/16/Z). LP is also supported by the UKRI through the JUNIPER modelling consortium (grant number MR/V038613/1) and by The Alan Turing Institute for Data Science and Artificial Intelligence. HBS is funded by the Wellcome Trust and Royal Society (202562/Z/16/Z), and the Alexander von Humboldt Foundation. DV had support from the National Council for Scientific and Technological Development of Brazil (CNPq - Refs. 441057/2020-9, 424141/2018-3, 309569/2019-2). FS is supported by the UKRI through the JUNIPER modelling consortium (grant number MR/V038613/1). EF is supported by UKRI (Medical Research Council)/Department of Health and Social Care (National Insitute of Health Research) MR/V028618/1. JPG's work was supported by funding from the UK Health Security Agency and the UK Department of Health and Social Care. Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross-disciplinary collaboration together with close communication between scientists and policy makers. Publisher PDF

A range of measures have been implemented to control within-school SARS-CoV-2 transmission in England, including the self-isolation of close contacts and twice weekly mass testing of secondary school pupils using lateral flow device tests (LFTs). Despite reducing transmission, isolating close contacts can lead to high levels of absences, negatively impacting pupils. To quantify pupil-to-pupil SARS-CoV-2 transmission and the impact of implemented control measures, we fit a stochastic individual-based model of secondary school infection to both swab testing data and secondary school absences data from England, and then simulate outbreaks from 31st August 2020 until 23rd May 2021. We find that the pupil-to-pupil reproduction number, Rschool, has remained below 1 on average across the study period, and that twice weekly mass testing using LFTs has helped to control pupil-to-pupil transmission. We also explore the potential benefits of alternative containment strategies, finding that a strategy of repeat testing of close contacts rather than isolation, alongside mass testing, substantially reduces absences with only a marginal increase in pupil-to-pupil transmission.

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritize some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritization include strategies that target those regions most at risk of importing the pathogen, and strategies that target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network and vaccine availability. We conclude that when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

The emergence of infectious agents with pandemic potential present scientific challenges from detection to data interpretation to understanding determinants of risk and forecasts. Mathematical models could play an essential role in how we prepare for future emergent pathogens. Here, we describe core directions for expansion of the existing tools and knowledge base, including: using mathematical models to identify critical directions and paths for strengthening data collection to detect and respond to outbreaks of novel pathogens; expanding basic theory to identify infectious agents and contexts that present the greatest risks, over both the short and longer term; by strengthening estimation tools that make the most use of the likely range and uncertainties in existing data; and by ensuring modelling applications are carefully communicated and developed within diverse and equitable collaborations for increased public health benefit.

Background The reduction in SARS-CoV-2 transmission facilitated by mobile contact tracing applications (apps) depends both on the proportion of relevant contacts notified and on the probability that those contacts quarantine after notification. The proportion of relevant contacts notified depends upon the number of days preceding an infector’s positive test that their contacts are notified, which we refer to as an app’s notification window. Methods We use an epidemiological model of SARS-CoV-2 transmission that captures the profile of infection to consider the trade-off between notification window length and active app use. We focus on 5-day and 2-day windows, the notification windows of the NHS COVID-19 app in England and Wales before and after 2nd August 2021, respectively. Results Our analyses show that at the same level of active app use, 5-day windows result in larger reductions in transmission than 2-day windows. However, short notification windows can be more effective at reducing transmission if they are associated with higher levels of active app use and adherence to isolation upon notification. Conclusions Our results demonstrate the importance of understanding adherence to interventions when setting notification windows for COVID-19 contact tracing apps.

In many countries, an extensive vaccination programme has substantially reduced the public-health impact of SARS-CoV-2, limiting the number of hospital admissions and deaths compared to an unmitigated epidemic. Ensuring a low-risk transition from the current situation to one in which SARS-CoV-2 is endemic requires maintenance of high levels of population immunity. The observed waning of vaccine efficacy over time suggests that booster doses may be required to maintain population immunity especially in the most vulnerable groups. Here, using data and models for England, we consider the dynamics of COVID-19 over a two-year time-frame, and the role that booster vaccinations can play in mitigating the worst effects. We find that boosters are necessary to suppress the imminent wave of infections that would be generated by waning vaccine efficacy. Projecting further into the future, the optimal deployment of boosters is highly sensitive to their long-term action. If protection from boosters wanes slowly (akin to protection following infection) then a single booster dose to the over 50s may be all that is needed over the next two-years. However, if protection wanes more rapidly (akin to protection following second dose vaccination) then annual or even biannual boosters are required to limit subsequent epidemic peaks an reduce the pressure on public health services.

SummaryBackgroundIn May 2021, the Delta SARS-CoV-2 variant became dominant in the UK. This variant is associated with increased transmissibility compared to the Alpha variant that was previously dominant. To understand ongoing transmission and interventions, a key question is whether the Delta variant generation time (the time between infections in infector- infectee pairs) is typically shorter–i.e., transmissions are happening more quickly–or whether infected individuals simply generate more infections.MethodsWe analysed transmission data from a UK Health Security Agency household study. By fitting a mathematical transmission model to the data, we estimated the generation times for the Alpha and Delta variants.ResultsThe mean intrinsic generation time (the generation time if there had been a constant supply of susceptibles throughout infection) was shorter for the Delta variant (4·6 days, 95% CrI 4·0-5·4 days) than the Alpha variant (5·5 days, 95% CrI 4·6-6·4 days), although within uncertainty ranges. However, there was a larger difference in the realised mean household generation time between the Delta (3·2 days, 95% CrI 2·4-4·2 days) and Alpha (4·5 days, 95% CrI 3·7-5·4 days) variants. This is because higher transmissibility led to faster susceptible depletion in households, in addition to the reduced intrinsic generation time.ConclusionsThe Delta variant transmits more quickly than previously circulating variants. This has implications for interventions such as contact tracing, testing and isolation, which are less effective if the virus is transmitted quickly. Epidemiological models of interventions should be updated to include the shorter generation time of the Delta variant.

BackgroundThunderstorm asthma is often characterised by a sudden surge in patients presenting with exacerbated symptoms of asthma linked to thunderstorm activity. On 17 June 2021, Public Health England (PHE) observed a large spike in health care seeking behaviour by patients presenting with asthma and difficulty breathing symptoms across parts of England.ObjectivesTo describe the epidemiology of the observed asthma spike and explore available meteorological and environmental data to understand potential causes of this episode.DesignA retrospective observational study was conducted of patient visits to health care services in England as monitored through surveillance systems routinely operated by PHE. The number of presentations during the asthma event was compared to expected levels for the overall population and across specific regions.SettingHealthcare services in England.Main outcome measuresNumber of patients presenting to healthcare services for asthma- and difficulty breathing-type symptoms.ResultsSpikes in asthma and difficulty breathing were detected across several PHE syndromic surveillance systems. Across affected areas ED attendances for asthma increased by 560% on 17 June compared to the average number of weekday daily attendances during the previous 4 weeks. GP out of hours contacts increased by 422%, NHS 111 calls 193%, NHS 111 online assessments 581% and ambulance call outs 54%. Increases were particularly noted in patient age groups 5-14 and 15-44 years. In non-affected regions, increases were small (ConclusionsAn unprecedented episode of asthma was recorded in England, characterised by significant surges in health care seeking behaviour. However, the links to meteorologically defined thunderstorm activity were not as clear as previous episodes, with less evidence of severe thunderstorm activity in those areas affected, prompting further discussion about the causes of these events and implications for public health management of the risk.

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed. Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel. We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility. Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high. The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain. Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.

African swine fever (ASF), caused by the African swine fever virus (ASFV), is highly virulent in domestic pigs and wild boar (Sus scrofa), causing up to 100% mortality. The recent epidemic of ASF in Europe has had a serious economic impact and poses a threat to global food security. Unfortunately, there is no effective treatment or vaccine against ASFV, limiting the available disease management strategies. Mathematical models allow us to further our understanding of infectious disease dynamics and evaluate the efficacy of disease management strategies. The ASF Challenge, organised by the French National Research Institute for Agriculture, Food, and the Environment, aimed to expand the development of ASF transmission models to inform policy makers in a timely manner. Here, we present the model and associated projections produced by our team during the challenge. We developed a stochastic model combining transmission between wild boar and domestic pigs, which was calibrated to synthetic data corresponding to different phases describing the epidemic progression. The model was then used to produce forward projections describing the likely temporal evolution of the epidemic under various disease management scenarios. Despite the interventions implemented, long-term projections forecasted persistence of ASFV in wild boar, and hence repeated outbreaks in domestic pigs. A key finding was that it is important to consider the timescale over which different measures are evaluated: interventions that have only limited effectiveness in the short term may yield substantial long-term benefits. Our model has several limitations, partly because it was developed in real-time. Nonetheless, it can inform understanding of the likely development of ASF epidemics and the efficacy of disease management strategies, should the virus continue its spread in Europe.\ud

Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

Funder: NHS Global Digital Exemplar programme, Funder: James S. McDonnell Foundation; FundRef: https://doi.org/10.13039/100000913, Funder: NIHR Health Protection Research Unit in Behavioural Science and Evaluation at the University of Bristol, Funder: Wellcome Trust; FundRef: https://doi.org/10.13039/100004440, Funder: Canadian Institutes for Health Research, Funder: Natural Science and Engineering Research Council of Canada, Since the beginning of the COVID-19 pandemic, the reproduction number [Formula: see text] has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, [Formula: see text] is defined as the average number of secondary infections caused by one primary infected individual. [Formula: see text] seems convenient, because the epidemic is expanding if [Formula: see text] and contracting if [Formula: see text]. The magnitude of [Formula: see text] indicates by how much transmission needs to be reduced to control the epidemic. Using [Formula: see text] in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of [Formula: see text] but many, and the precise definition of [Formula: see text] affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined [Formula: see text], there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate [Formula: see text] vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when [Formula: see text] is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of [Formula: see text], and the data and methods used to estimate it, can make [Formula: see text] a more useful metric for future management of the epidemic.

When vaccinating a large population in response to an invading pathogen, it is often necessary to prioritise some individuals to be vaccinated first. One way to do this is to choose individuals to vaccinate based on their location. Methods for this prioritisation include strategies which target those regions most at risk of importing the pathogen, and strategies which target regions with high centrality on the travel network. We use a simple infectious disease epidemic model to compare a risk-targeting strategy to two different centrality-targeting strategies based on betweenness centrality and random walk percolation centrality, respectively. We find that the relative effectiveness of these strategies in reducing the total number of infections varies with the basic reproduction number of the pathogen, travel rates, structure of the travel network, and vaccine availability. We conclude that, when a pathogen has high spreading capacity, or when vaccine availability is limited, centrality-targeting strategies should be considered as an alternative to the more commonly used risk-targeting strategies.

As a countermeasure to the SARS-CoV-2 pandemic, there has been swift development and clinical trial assessment of candidate vaccines, with subsequent deployment as part of mass vaccination campaigns. However, the SARS-CoV-2 virus has demonstrated the ability to mutate and develop variants, which can modify epidemiological properties and potentially also the effectiveness of vaccines. The widespread deployment of highly effective vaccines may rapidly exert selection pressure on the SARS-CoV-2 virus directed towards mutations that escape the vaccine-induced immune response. This is particularly concerning while infection is widespread. By developing and analysing a mathematical model of two population groupings with differing vulnerability and contact rates, we explore the impact of the deployment of vaccines among the population on the reproduction ratio, cases, disease abundance and vaccine escape pressure. The results from this model illustrate two insights: (i) vaccination aimed at reducing prevalence could be more effective at reducing disease than directly vaccinating the vulnerable; (ii) the highest risk for vaccine escape can occur at intermediate levels of vaccination. This work demonstrates a key principle: the careful targeting of vaccines towards particular population groups could reduce disease as much as possible while limiting the risk of vaccine escape.

BackgroundTo control within-school SARS-CoV-2 transmission in England, secondary school pupils have been encouraged to participate in twice weekly mass testing via lateral flow device tests (LFTs) from 8th March 2021, to complement an isolation of close contacts policy in place since 31st August 2020. Strategies involving the isolation of close contacts can lead to high levels of absences, negatively impacting pupils.MethodsWe fit a stochastic individual-based model of secondary schools to both community swab testing data and secondary school absences data. By simulating epidemics in secondary schools from 31st August 2020 until 21st May 2021, we quantify within-school transmission of SARS-CoV-2 in secondary schools in England, the impact of twice weekly mass testing on within-school transmission, and the potential impact of alternative strategies to the isolation of close contacts in reducing pupil absences.FindingsThe within-school reproduction number, Rschool, has remained below 1 from 31st August 2020 until 21st May 2021. Twice weekly mass testing using LFTs have helped to control within-school transmission in secondary schools in England. A strategy of serial contact testing alongside mass testing substantially reduces absences compared to strategies involving isolating close contacts, with only a marginal increase in within-school transmission.InterpretationSecondary school control strategies involving mass testing have the potential to control within-school transmission while substantially reducing absences compared to an isolation of close contacts policy.

[Background] Development of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials. [Methods and findings] A modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d−1 (95% CI: 1.06 to 1.27 d−1), 0.777 d−1 (0.716 to 0.838 d−1), and 0.450 d−1 (0.378 to 0.522 d−1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13, 603 and 11, 670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation. [Conclusions] In this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model., 数理モデルによる臨床試験シミュレータを開発 --感染症に対する標準治療法の早期確立に貢献--. 京都大学プレスリリース. 2021-07-07., Setting COVID-19 drug trials up for success. 京都大学プレスリリース. 2021-07-07.

The distribution of the generation time (the interval between individuals becoming infected and passing on the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to SARS-CoV-2 data from January-March 2020 compared to existing models. However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March-November 2020 in the UK, we provide updated estimates of the generation time. We consider both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% CrI 3.3-5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0-8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (6.0 days, 5.2-7.0 days) and a similar standard deviation (4.9 days, 4.0-6.3 days). Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, continued data collection and analysis is necessary to inform future public health policy decisions.

The distribution of the generation time (the interval between individuals becoming infected and transmitting the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to data from the early months of the COVID-19 pandemic (December 2019-March 2020) compared to existing models (Hart et al., 2021). However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March to November 2020 in the UK, we provide updated estimates of the generation time. We considered both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% credible interval 3.3–5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0–8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (5.9 days, 5.2–7.0 days) and a similar standard deviation (4.8 days, 4.0–6.3 days). As well as estimating the generation time using data from the entire study period, we also considered whether the generation time varied temporally. Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, further data collection and analysis is necessary to continue to monitor ongoing transmission and inform future public health policy decisions.

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed. Here, using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases introduced into new locations initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel. Rather than aiming to make exact quantitative predictions about the outbreak risk in different locations, we instead use data from these locations to demonstrate the general principle that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed in low prevalence settings. This conclusion holds even once vaccine programmes are completed. Key factors underlying these results are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility. Combined, these factors suggest that when travel restrictions are relaxed, it will still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, should remain in place to suppress potential outbreaks until case numbers globally are reduced.