• A massively multi-scale approach to characterizing tissue architecture by synchrotron micro-CT applied to the human placenta

      Tun, W. M.; orcid: 0000-0003-0991-8785; Poologasundarampillai, G.; orcid: 0000-0002-8498-323X; Bischof, H.; Nye, G.; King, O. N. F.; orcid: 0000-0002-6152-7207; Basham, M.; orcid: 0000-0002-8438-1415; Tokudome, Y.; Lewis, R. M.; orcid: 0000-0003-4044-9104; Johnstone, E. D.; Brownbill, P.; orcid: 0000-0002-8328-7072; email: paul.brownbill@manchester.ac.uk; et al. (The Royal Society, 2021-06-02)
      Multi-scale structural assessment of biological soft tissue is challenging but essential to gain insight into structure–function relationships of tissue/organ. Using the human placenta as an example, this study brings together sophisticated sample preparation protocols, advanced imaging and robust, validated machine-learning segmentation techniques to provide the first massively multi-scale and multi-domain information that enables detailed morphological and functional analyses of both maternal and fetal placental domains. Finally, we quantify the scale-dependent error in morphological metrics of heterogeneous placental tissue, estimating the minimal tissue scale needed in extracting meaningful biological data. The developed protocol is beneficial for high-throughput investigation of structure–function relationships in both normal and diseased placentas, allowing us to optimize therapeutic approaches for pathological pregnancies. In addition, the methodology presented is applicable in the characterization of tissue architecture and physiological behaviours of other complex organs with similarity to the placenta, where an exchange barrier possesses circulating vascular and avascular fluid spaces.
    • A massively multi-scale approach to characterizing tissue architecture by synchrotron micro-CT applied to the human placenta

      Tun, W. M.; orcid: 0000-0003-0991-8785; Poologasundarampillai, G.; orcid: 0000-0002-8498-323X; Bischof, H.; Nye, G.; King, O. N. F.; orcid: 0000-0002-6152-7207; Basham, M.; orcid: 0000-0002-8438-1415; Tokudome, Y.; Lewis, R. M.; orcid: 0000-0003-4044-9104; Johnstone, E. D.; Brownbill, P.; orcid: 0000-0002-8328-7072; et al. (The Royal Society, 2021-06-02)
      Multi-scale structural assessment of biological soft tissue is challenging but essential to gain insight into structure–function relationships of tissue/organ. Using the human placenta as an example, this study brings together sophisticated sample preparation protocols, advanced imaging and robust, validated machine-learning segmentation techniques to provide the first massively multi-scale and multi-domain information that enables detailed morphological and functional analyses of both maternal and fetal placental domains. Finally, we quantify the scale-dependent error in morphological metrics of heterogeneous placental tissue, estimating the minimal tissue scale needed in extracting meaningful biological data. The developed protocol is beneficial for high-throughput investigation of structure–function relationships in both normal and diseased placentas, allowing us to optimize therapeutic approaches for pathological pregnancies. In addition, the methodology presented is applicable in the characterization of tissue architecture and physiological behaviours of other complex organs with similarity to the placenta, where an exchange barrier possesses circulating vascular and avascular fluid spaces.
    • Adaptation at different points along antibiotic concentration gradients

      Lagator, Mato; orcid: 0000-0001-7847-3594; email: mato.lagator@manchester.ac.uk; Uecker, Hildegard; orcid: 0000-0001-9435-2813; Neve, Paul (The Royal Society, 2021-05-12)
      Antibiotic concentrations vary dramatically in the body and the environment. Hence, understanding the dynamics of resistance evolution along antibiotic concentration gradients is critical for predicting and slowing the emergence and spread of resistance. While it has been shown that increasing the concentration of an antibiotic slows resistance evolution, how adaptation to one antibiotic concentration correlates with fitness at other points along the gradient has not received much attention. Here, we selected populations of Escherichia coli at several points along a concentration gradient for three different antibiotics, asking how rapidly resistance evolved and whether populations became specialized to the antibiotic concentration they were selected on. Populations selected at higher concentrations evolved resistance more slowly but exhibited equal or higher fitness across the whole gradient. Populations selected at lower concentrations evolved resistance rapidly, but overall fitness in the presence of antibiotics was lower. However, these populations readily adapted to higher concentrations upon subsequent selection. Our results indicate that resistance management strategies must account not only for the rates of resistance evolution but also for the fitness of evolved strains.
    • Basil Lythgoe. 18 August 1913—18 April 2009

      Jones, J. C. (The Royal Society, 2021-03-03)
      Basil Lythgoe was distinguished as an organic chemist. He began his career at the University of Manchester, where he had studied for his undergraduate and PhD degrees, before moving to University of Cambridge. During this period he collaborated with Alexander Todd on the structural elucidation and total synthesis of the natural nucleosides, and was also noted for his investigation of the structure of the natural substance macrozamin. In 1953 he moved to the chair of organic chemistry at the University of Leeds, running a research group from which several graduate students went on to academic careers of the highest distinction. At Leeds he worked on the structure of the alkaloid taxine 1 and calciferol, among other natural substances. Lythgoe's work was characterized by a combination of insight and high experimental skill.
    • Basil Lythgoe. 18 August 1913—18 April 2009

      Jones, J. C. (The Royal Society, 2021-03-03)
      Basil Lythgoe was distinguished as an organic chemist. He began his career at the University of Manchester, where he had studied for his undergraduate and PhD degrees, before moving to University of Cambridge. During this period he collaborated with Alexander Todd on the structural elucidation and total synthesis of the natural nucleosides, and was also noted for his investigation of the structure of the natural substance macrozamin. In 1953 he moved to the chair of organic chemistry at the University of Leeds, running a research group from which several graduate students went on to academic careers of the highest distinction. At Leeds he worked on the structure of the alkaloid taxine 1 and calciferol, among other natural substances. Lythgoe's work was characterized by a combination of insight and high experimental skill.
    • Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

      Pellis, Lorenzo; orcid: 0000-0002-3436-6487; email: lorenzo.pellis@manchester.ac.uk; Scarabel, Francesca; orcid: 0000-0003-0250-4555; Stage, Helena B.; orcid: 0000-0001-9938-8452; Overton, Christopher E.; Chappell, Lauren H. K.; Fearon, Elizabeth; Bennett, Emma; Lythgoe, Katrina A.; House, Thomas A.; orcid: 0000-0001-5835-8062; Hall, Ian; orcid: 0000-0002-3033-2335; et al. (The Royal Society, 2021-05-31)
      Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2–4.3 days) and Italian hospital and intensive care unit admissions every 2–3 days; values that are significantly lower than the 5–7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

      Pellis, Lorenzo; orcid: 0000-0002-3436-6487; email: lorenzo.pellis@manchester.ac.uk; Scarabel, Francesca; orcid: 0000-0003-0250-4555; Stage, Helena B.; orcid: 0000-0001-9938-8452; Overton, Christopher E.; orcid: 0000-0002-8433-4010; Chappell, Lauren H. K.; orcid: 0000-0001-8654-2756; Fearon, Elizabeth; orcid: 0000-0001-5574-251X; Bennett, Emma; orcid: 0000-0001-7188-4315; Lythgoe, Katrina A.; orcid: 0000-0002-7089-7680; House, Thomas A.; orcid: 0000-0001-5835-8062; Hall, Ian; orcid: 0000-0002-3033-2335; et al. (The Royal Society, 2021-05-31)
      Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2–4.3 days) and Italian hospital and intensive care unit admissions every 2–3 days; values that are significantly lower than the 5–7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

      Pellis, Lorenzo; orcid: 0000-0002-3436-6487; email: lorenzo.pellis@manchester.ac.uk; Scarabel, Francesca; orcid: 0000-0003-0250-4555; Stage, Helena B.; orcid: 0000-0001-9938-8452; Overton, Christopher E.; orcid: 0000-0002-8433-4010; Chappell, Lauren H. K.; orcid: 0000-0001-8654-2756; Fearon, Elizabeth; orcid: 0000-0001-5574-251X; Bennett, Emma; orcid: 0000-0001-7188-4315; Lythgoe, Katrina A.; orcid: 0000-0002-7089-7680; House, Thomas A.; orcid: 0000-0001-5835-8062; Hall, Ian; orcid: 0000-0002-3033-2335; et al. (The Royal Society, 2021-05-31)
      Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2–4.3 days) and Italian hospital and intensive care unit admissions every 2–3 days; values that are significantly lower than the 5–7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number R0 for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of R0 alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Convex hull estimation of mammalian body segment parameters

      Coatham, Samuel J.; orcid: 0000-0003-4597-6210; email: sam.coatham@postgrad.manchester.ac.uk; Sellers, William I.; orcid: 0000-0002-2913-5406; Püschel, Thomas A.; orcid: 0000-0002-2231-2297 (The Royal Society, 2021-06-30)
      Obtaining accurate values for body segment parameters (BSPs) is fundamental in many biomechanical studies, particularly for gait analysis. Convex hulling, where the smallest-possible convex object that surrounds a set of points is calculated, has been suggested as an effective and time-efficient method to estimate these parameters in extinct animals, where soft tissues are rarely preserved. We investigated the effectiveness of convex hull BSP estimation in a range of extant mammals, to inform the potential future usage of this technique with extinct taxa. Computed tomography scans of both the skeleton and skin of every species investigated were virtually segmented. BSPs (the mass, position of the centre of mass and inertial tensors of each segment) were calculated from the resultant soft tissue segments, while the bone segments were used as the basis for convex hull reconstructions. We performed phylogenetic generalized least squares and ordinary least squares regressions to compare the BSPs calculated from soft tissue segments with those estimated using convex hulls, finding consistent predictive relationships for each body segment. The resultant regression equations can, therefore, be used with confidence in future volumetric reconstruction and biomechanical analyses of mammals, in both extinct and extant species where such data may not be available.
    • Inferring kinetic parameters of oscillatory gene regulation from single cell time-series data

      Burton, Joshua; orcid: 0000-0001-8530-0464; Manning, Cerys S.; orcid: 0000-0001-8656-5878; Rattray, Magnus; orcid: 0000-0001-8196-5565; Papalopulu, Nancy; orcid: 0000-0001-6992-6870; email: Nancy.Papalopulu@manchester.ac.uk; Kursawe, Jochen; orcid: 0000-0002-0314-9623; email: jochen.kursawe@st-andrews.ac.uk (The Royal Society, 2021-09-29)
      Gene expression dynamics, such as stochastic oscillations and aperiodic fluctuations, have been associated with cell fate changes in multiple contexts, including development and cancer. Single cell live imaging of protein expression with endogenous reporters is widely used to observe such gene expression dynamics. However, the experimental investigation of regulatory mechanisms underlying the observed dynamics is challenging, since these mechanisms include complex interactions of multiple processes, including transcription, translation and protein degradation. Here, we present a Bayesian method to infer kinetic parameters of oscillatory gene expression regulation using an auto-negative feedback motif with delay. Specifically, we use a delay-adapted nonlinear Kalman filter within a Metropolis-adjusted Langevin algorithm to identify posterior probability distributions. Our method can be applied to time-series data on gene expression from single cells and is able to infer multiple parameters simultaneously. We apply it to published data on murine neural progenitor cells and show that it outperforms alternative methods. We further analyse how parameter uncertainty depends on the duration and time resolution of an imaging experiment, to make experimental design recommendations. This work demonstrates the utility of parameter inference on time course data from single cells and enables new studies on cell fate changes and population heterogeneity.
    • Making the most of potential: potential games and genotypic convergence

      Edhan, Omer; orcid: 0000-0002-4441-3304; email: omeredhan.idan@manchester.ac.uk; Hellman, Ziv; orcid: 0000-0002-2624-0577; Nehama, Ilan; orcid: 0000-0002-4152-4113 (The Royal Society, 2021-08-25)
      We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.
    • Making the most of potential: potential games and genotypic convergence

      Edhan, Omer; orcid: 0000-0002-4441-3304; email: omeredhan.idan@manchester.ac.uk; Hellman, Ziv; orcid: 0000-0002-2624-0577; Nehama, Ilan; orcid: 0000-0002-4152-4113 (The Royal Society, 2021-08-25)
      We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.
    • Methods for quantifying methane emissions using unmanned aerial vehicles: a review

      Shaw, Jacob T.; orcid: 0000-0003-3558-3894; email: jacob.shaw@manchester.ac.uk; Shah, Adil; orcid: 0000-0002-5692-3715; Yong, Han; Allen, Grant; orcid: 0000-0002-7070-3620; email: grant.allen@manchester.ac.uk (The Royal Society, 2021-09-27)
      Methane is an important greenhouse gas, emissions of which have vital consequences for global climate change. Understanding and quantifying the sources (and sinks) of atmospheric methane is integral for climate change mitigation and emission reduction strategies, such as those outlined in the 2015 UN Paris Agreement on Climate Change. There are ongoing international efforts to constrain the global methane budget, using a wide variety of measurement platforms across a range of spatial and temporal scales. The advancements in unmanned aerial vehicle (UAV) technology over the past decade have opened up a new avenue for methane emission quantification. UAVs can be uniquely equipped to monitor natural and anthropogenic emissions at local scales, displaying clear advantages in versatility and manoeuvrability relative to other platforms. Their use is not without challenge, however: further miniaturization of high-performance methane instrumentation is needed to fully use the benefits UAVs afford. Developments in the models used to simulate atmospheric transport and dispersion across small, local scales are also crucial to improved flux accuracy and precision. This paper aims to provide an overview of currently available UAV-based technologies and sampling methodologies which can be used to quantify methane emission fluxes at local scales. This article is part of a discussion meeting issue 'Rising methane: is warming feeding warming? (part 1)'.
    • Outbreaks in care homes may lead to substantial disease burden if not mitigated

      Hall, Ian; orcid: 0000-0002-3033-2335; email: ian.hall@manchester.ac.uk; Lewkowicz, Hugo; orcid: 0000-0002-8944-0365; Webb, Luke; orcid: 0000-0001-6263-0575; House, Thomas; orcid: 0000-0001-5835-8062; Pellis, Lorenzo; orcid: 0000-0002-3436-6487; Sedgwick, James; orcid: 0000-0002-7200-4559; Gent, Nick; orcid: 0000-0002-2605-7369; on behalf of the University of Manchester COVID-19 Modelling Group and the Public Health England Modelling Team (The Royal Society, 2021-05-31)
      The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Outbreaks in care homes may lead to substantial disease burden if not mitigated

      Hall, Ian; orcid: 0000-0002-3033-2335; email: ian.hall@manchester.ac.uk; Lewkowicz, Hugo; orcid: 0000-0002-8944-0365; Webb, Luke; orcid: 0000-0001-6263-0575; House, Thomas; orcid: 0000-0001-5835-8062; Pellis, Lorenzo; orcid: 0000-0002-3436-6487; Sedgwick, James; orcid: 0000-0002-7200-4559; Gent, Nick; orcid: 0000-0002-2605-7369; on behalf of the University of Manchester COVID-19 Modelling Group and the Public Health England Modelling Team (The Royal Society, 2021-05-31)
      The number of COVID-19 outbreaks reported in UK care homes rose rapidly in early March of 2020. Owing to the increased co-morbidities and therefore worse COVID-19 outcomes for care home residents, it is important that we understand this increase and its future implications. We demonstrate the use of an SIS model where each nursing home is an infective unit capable of either being susceptible to an outbreak (S) or in an active outbreak (I). We use a generalized additive model to approximate the trend in growth rate of outbreaks in care homes and find the fit to be improved in a model where the growth rate is proportional to the number of current care home outbreaks compared with a model with a constant growth rate. Using parameters found from the outbreak-dependent growth rate, we predict a 73% prevalence of outbreaks in UK care homes without intervention as a reasonable worst-case planning assumption. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Palladium-doped hierarchical ZSM-5 for catalytic selective oxidation of allylic and benzylic alcohols

      Ding, Shengzhe; orcid: 0000-0003-2822-3882; Ganesh, Muhammad; Jiao, Yilai; Ou, Xiaoxia; Isaacs, Mark A.; orcid: 0000-0002-0335-4272; S'ari, Mark; Torres Lopez, Antonio; orcid: 0000-0001-7378-1811; Fan, Xiaolei; orcid: 0000-0002-9039-6736; email: xiaolei.fan@manchester.ac.uk; Parlett, Christopher M. A.; orcid: 0000-0002-3651-7314; email: christopher.parlett@manchester.ac.uk (The Royal Society, 2021-10-20)
      Hierarchical zeolites have the potential to provide a breakthrough in transport limitation, which hinders pristine microporous zeolites and thus may broaden their range of applications. We have explored the use of Pd-doped hierarchical ZSM-5 zeolites for aerobic selective oxidation (selox) of cinnamyl alcohol and benzyl alcohol to their corresponding aldehydes. Hierarchical ZSM-5 with differing acidity (H-form and Na-form) were employed and compared with two microporous ZSM-5 equivalents. Characterization of the four catalysts by X-ray diffraction, nitrogen porosimetry, NH3 temperature-programmed desorption, CO chemisorption, high-resolution scanning transmission electron microscopy, X-ray photoelectron spectroscopy and X-ray absorption spectroscopy allowed investigation of their porosity, acidity, as well as Pd active sites. The incorporation of complementary mesoporosity, within the hierarchical zeolites, enhances both active site dispersion and PdO active site generation. Likewise, alcohol conversion was also improved with the presence of secondary mesoporosity, while strong Brønsted acidity, present solely within the H-form systems, negatively impacted overall selectivity through undesirable self-etherification. Therefore, tuning support porosity and acidity alongside active site dispersion is paramount for optimal aldehyde production.
    • Scalability of resonant motor-driven flapping wing propulsion systems

      Nabawy, Mostafa R. A.; orcid: 0000-0002-4252-1635; email: mostafa.ahmednabawy@manchester.ac.uk; Marcinkeviciute, Ruta (The Royal Society, 2021-09-22)
      This work aims to develop an integrated conceptual design process to assess the scalability and performance of propulsion systems of resonant motor-driven flapping wing vehicles. The developed process allows designers to explore the interaction between electrical, mechanical and aerodynamic domains in a single transparent design environment. Wings are modelled based on a quasi-steady treatment that evaluates aerodynamics from geometry and kinematic information. System mechanics is modelled as a damped second-order dynamic system operating at resonance with nonlinear aerodynamic damping. Motors are modelled using standard equations that relate operational parameters and AC voltage input. Design scaling laws are developed using available data based on current levels of technology. The design method provides insights into the effects of changing core design variables such as the actuator size, actuator mass fraction and pitching kinematics on the overall design solution. It is shown that system efficiency achieves peak values of 30–36% at motor masses of 0.5–1 g when a constant angle of attack kinematics is employed. While sinusoidal angle of attack kinematics demands more aerodynamic and electric powers compared with the constant angle of attack case, sinusoidal angle of attack kinematics can lead to a maximum difference of around 15% in peak system efficiency.
    • Shut and re-open: the role of schools in the spread of COVID-19 in Europe

      Stage, Helena B.; orcid: 0000-0001-9938-8452; email: helena.stage@manchester.ac.uk; Shingleton, Joseph; orcid: 0000-0002-1628-3231; email: Joseph.Shingleton@phe.gov.uk; Ghosh, Sanmitra; orcid: 0000-0002-4879-7587; Scarabel, Francesca; orcid: 0000-0003-0250-4555; Pellis, Lorenzo; orcid: 0000-0002-3436-6487; Finnie, Thomas; orcid: 0000-0001-5962-4211 (The Royal Society, 2021-05-31)
      We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases under different interventions, we provide evidence that school closures contribute to a reduction in the growth rate approximately 7 days after implementation. Limited school attendance, such as older students sitting exams or the partial return of younger year groups, does not appear to significantly affect community transmission. In countries where community transmission is generally low, such as Denmark or Norway, a large-scale reopening of schools while controlling or suppressing the epidemic appears feasible. However, school reopening can contribute to statistically significant increases in the growth rate in countries like Germany, where community transmission is relatively high. In all regions, a combination of low classroom occupancy and robust test-and-trace measures were in place. Our findings underscore the need for a cautious evaluation of reopening strategies. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • Shut and re-open: the role of schools in the spread of COVID-19 in Europe

      Stage, Helena B.; orcid: 0000-0001-9938-8452; email: helena.stage@manchester.ac.uk; Shingleton, Joseph; orcid: 0000-0002-1628-3231; email: Joseph.Shingleton@phe.gov.uk; Ghosh, Sanmitra; orcid: 0000-0002-4879-7587; Scarabel, Francesca; orcid: 0000-0003-0250-4555; Pellis, Lorenzo; orcid: 0000-0002-3436-6487; Finnie, Thomas; orcid: 0000-0001-5962-4211 (The Royal Society, 2021-05-31)
      We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases under different interventions, we provide evidence that school closures contribute to a reduction in the growth rate approximately 7 days after implementation. Limited school attendance, such as older students sitting exams or the partial return of younger year groups, does not appear to significantly affect community transmission. In countries where community transmission is generally low, such as Denmark or Norway, a large-scale reopening of schools while controlling or suppressing the epidemic appears feasible. However, school reopening can contribute to statistically significant increases in the growth rate in countries like Germany, where community transmission is relatively high. In all regions, a combination of low classroom occupancy and robust test-and-trace measures were in place. Our findings underscore the need for a cautious evaluation of reopening strategies. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.
    • The Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods

      Kisil, Anastasia V.; orcid: 0000-0001-7652-5880; email: anastasia.kisil@manchester.ac.uk; Abrahams, I. David; Mishuris, Gennady; orcid: 0000-0003-2565-1961; Rogosin, Sergei V.; orcid: 0000-0002-7356-1656 (The Royal Society, 2021-10-20)
      This paper reviews the modern state of the Wiener–Hopf factorization method and its generalizations. The main constructive results for matrix Wiener–Hopf problems are presented, approximate methods are outlined and the main areas of applications are mentioned. The aim of the paper is to offer an overview of the development of this method, and demonstrate the importance of bringing together pure and applied analysis to effectively employ the Wiener–Hopf technique.