Ageing in Mortal Superdiffusive L\'evy Walkers

A growing body of literature examines the effects of superdiffusive subballistic movement pre-measurement (ageing or time lag) on observations arising from single-particle tracking. A neglected aspect is the finite lifetime of these L\'{e}vy walkers, be they proteins, cells or larger structures. We examine the effects of ageing on the motility of mortal walkers, and discuss the means by which permanent stopping of walkers may be categorised as arising from `natural' death or experimental artefacts such as low photostability or radiation damage. This is done by comparison of the walkers' mean squared displacement (MSD) with the front velocity of propagation of a group of walkers, which is found to be invariant under time lags. For any running time distribution of a mortal random walker, the MSD is tempered by the stopping rate $\theta$. This provides a physical interpretation for truncated heavy-tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers. Tempering of aged MSDs raises the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales

Shut and re-open: the role of schools in the spread of COVID-19 in Europe.

Funder: Department for Health and Social CareWe 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

From The Royal Society via Jisc Publications RouterHistory: accepted 2020-12-02, pub-electronic 2021-05-31, pub-print 2021-07-19Article version: VoRPublication status: PublishedFunder: Wellcome Trust; Id: http://dx.doi.org/10.13039/100004440; Grant(s): 202562/Z/16/ZFunder: Royal Society; Id: http://dx.doi.org/10.13039/501100000288; Grant(s): 202562/Z/16/ZFunder: Department for Health and Social CareFunder: Canadian Institutes of Health Research; Id: http://dx.doi.org/10.13039/501100000024; Grant(s): 2019 Novel Coronavirus (COVID-19) rapid researchFunder: Medical Research Council; Id: http://dx.doi.org/10.13039/501100000265; Grant(s): MC UU 00002/11We 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’

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

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 for modelling interventions for future pandemics

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 PDFPeer reviewe

The effectiveness of social bubbles as part of a Covid-19 lockdown exit strategy, a modelling study

Background: ​ During the coronavirus disease 2019 (COVID-19) lockdown, contact clustering in social bubbles may allow extending contacts beyond the household at minimal additional risk and hence has been considered as part of modified lockdown policy or a gradual lockdown exit strategy. We estimated the impact of such strategies on epidemic and mortality risk using the UK as a case study. Methods: ​ We used an individual based model for a synthetic population similar to the UK, stratified into transmission risks from the community, within the household and from other households in the same social bubble. The base case considers a situation where non-essential shops and schools are closed, the secondary household attack rate is 20% and the initial reproduction number is 0.8. We simulate social bubble strategies (where two households form an exclusive pair) for households including children, for single occupancy households, and for all households. We test the sensitivity of results to a range of alternative model assumptions and parameters. Results:  Clustering contacts outside the household into exclusive bubbles is an effective strategy of increasing contacts while limiting the associated increase in epidemic risk. In the base case, social bubbles reduced fatalities by 42% compared to an unclustered increase of contacts. We find that if all households were to form social bubbles the reproduction number would likely increase to above the epidemic threshold of R=1. Strategies allowing households with young children or single occupancy households to form social bubbles increased the reproduction number by less than 11%. The corresponding increase in mortality is proportional to the increase in the epidemic risk but is focussed in older adults irrespective of inclusion in social bubbles. Conclusions: ​ If managed appropriately, social bubbles can be an effective way of extending contacts beyond the household while limiting the increase in epidemic risk.</ns3:p

Challenges in control of COVID-19: short doubling time and long delay to effect of interventions

From The Royal Society via Jisc Publications RouterHistory: accepted 2021-04-21, pub-electronic 2021-05-31, pub-print 2021-07-19Article version: VoRPublication status: PublishedFunder: Wellcome Trust; Id: http://dx.doi.org/10.13039/100004440; Grant(s): 107652/Z/15/Z, 202562/Z/16/ZFunder: Institute of Population and Public Health; Id: http://dx.doi.org/10.13039/501100000036; Grant(s): CIHR 2019 Novel Coronavirus (COVID-19) rapid reseaFunder: National Institute for Health Research; Id: http://dx.doi.org/10.13039/501100000272Funder: Medical Research Council; Id: http://dx.doi.org/10.13039/501100000265; Grant(s): MR/S020462/1, MR/V038613/1Funder: Public Health Research Programme; Id: http://dx.doi.org/10.13039/501100001921Funder: Biotechnology and Biological Sciences Research Council; Id: http://dx.doi.org/10.13039/501100000268; Grant(s): BB/R009236/1Funder: Royal Society; Id: http://dx.doi.org/10.13039/501100000288; Grant(s): INF\R2\180067Funder: Alan Turing Institute; Id: http://dx.doi.org/10.13039/100012338Early 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’