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Acknowledgements: The authors would like to thank colleagues in SPI-M-O and JUNIPER consortium for various discussions around hospital modelling and forecasting., Funder: National Institute for Health Research Health Protection Research Unit (NIHR HPRU) in Emergency Preparedness and Response, Funder: Li Ka Shing Foundation; funder-id: http://dx.doi.org/10.13039/100007421, Funder: National Institute for Health Research Policy Research Programme in Operational Research (OPERA), The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

Quarantining close contacts of individuals infected with SARS-CoV-2 for 10 to 14 days is a key strategy in reducing transmission. However, quarantine requirements are often unpopular, with low adherence, especially when a large fraction of the population has been vaccinated. Daily contact testing (DCT), in which contacts are required to isolate only if they test positive, is an alternative to quarantine for mitigating the risk of transmission from traced contacts. In this study, we developed an integrated model of COVID-19 transmission dynamics and compared the strategies of quarantine and DCT with regard to reduction in transmission and social/economic costs (days of quarantine/self-isolation). Specifically, we compared 10-day quarantine to 7 days of self-testing using rapid lateral flow antigen tests, starting 3 days after exposure to a case. We modelled both incomplete adherence to quarantine and incomplete adherence to DCT. We found that DCT reduces transmission from contacts with similar effectiveness, at much lower social/economic costs, especially for highly vaccinated populations. The findings were robust across a spectrum of scenarios with varying assumptions on the speed of contact tracing, sensitivity of lateral flow antigen tests, adherence to quarantine and uptake of testing. Daily tests would also allow rapid initiation of a new round of tracing from infected contacts.

Contact tracing is increasingly used to combat COVID-19, and digital implementations are now being deployed, many based on Apple and Google’s Exposure Notification System. These systems utilize non-traditional smartphone-based technology, presenting challenges in understanding possible outcomes. In this work, we create individual-based models of three Washington state counties to explore how digital exposure notifications combined with other non-pharmaceutical interventions influence COVID-19 disease spread under various adoption, compliance, and mobility scenarios. In a model with 15% participation, we found that exposure notification could reduce infections and deaths by approximately 8% and 6% and could effectively complement traditional contact tracing. We believe this can provide health authorities in Washington state and beyond with guidance on how exposure notification can complement traditional interventions to suppress the spread of COVID-19.

We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov–Takens and zero-Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner., The research leading to these results has received funding from ‘la Caixa’ Foundation. This work has been also partially funded by the ‘María de Maeztu’ Programme for Units of Excellence in R&D (MDM-2014-0445), as well as from projects MTM2014-52209-C2-1-P and MTM2017-86795-C3-1-P from the Spanish MINECO, and from the CERCA Programme of the Generalitat de Catalunya. M.H. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 707658. Work in València was supported by Spain’s Agencia Estatal de Investigación - FEDER grant no. BFU2015-65037-P to S.F.E. J.S. has been also funded by a ‘Ramón y Cajal’ Fellowship (RYC-2017-22243).

SARS-CoV-2 has spread across the world, causing high mortality and unprecedented restrictions on social and economic activity. Policymakers are assessing how best to navigate through the ongoing epidemic, with models being used to predict the spread of infection and assess the impact of public health measures. Here, we present OpenABM-Covid19: an agent-based simulation of the epidemic including detailed age-stratification and realistic social networks. By default the model is parameterised to UK demographics and calibrated to the UK epidemic, however, it can easily be re-parameterised for other countries. OpenABM-Covid19 can evaluate non-pharmaceutical interventions, including both manual and digital contact tracing. It can simulate a population of 1 million people in seconds per day allowing parameter sweeps and formal statistical model-based inference. The code is open-source and has been developed by teams both inside and outside academia, with an emphasis on formal testing, documentation, modularity and transparency. A key feature of OpenABM-Covid19 is its Python interface, which has allowed scientists and policymakers to simulate dynamic packages of interventions and help compare options to suppress the COVID-19 epidemic.

Contact tracing is increasingly being used to combat COVID-19, and digital implementations are now being deployed, many of them based on Apple and Google’s Exposure Notification System. These systems are new and are based on smartphone technology that has not traditionally been used for this purpose, presenting challenges in understanding possible outcomes. In this work, we use individual-based computational models to explore how digital exposure notifications can be used in conjunction with non-pharmaceutical interventions, such as traditional contact tracing and social distancing, to influence COVID-19 disease spread in a population. Specifically, we use a representative model of the household and occupational structure of three counties in the state of Washington together with a proposed digital exposure notifications deployment to quantify impacts under a range of scenarios of adoption, compliance, and mobility. In a model in which 15% of the population participated, we found that digital exposure notification systems could reduce infections and deaths by approximately 8% and 6%, effectively complementing traditional contact tracing. We believe this can serve as guidance to health authorities in Washington state and beyond on how exposure notification systems can complement traditional public health interventions to suppress the spread of COVID-19.

Instantaneous contact tracing New analyses indicate that severe acute respiratory syndrome–coronavirus 2 (SARS-CoV-2) is more infectious and less virulent than the earlier SARS-CoV-1, which emerged in China in 2002. Unfortunately, the current virus has greater epidemic potential because it is difficult to trace mild or presymptomatic infections. As no treatment is currently available, the only tools that we can currently deploy to stop the epidemic are contact tracing, social distancing, and quarantine, all of which are slow to implement. However imperfect the data, the current global emergency requires more timely interventions. Ferretti et al. explored the feasibility of protecting the population (that is, achieving transmission below the basic reproduction number) using isolation coupled with classical contact tracing by questionnaires versus algorithmic instantaneous contact tracing assisted by a mobile phone application. For prevention, the crucial information is understanding the relative contributions of different routes of transmission. A phone app could show how finite resources must be divided between different intervention strategies for the most effective control. Science , this issue p. eabb6936

Background: The timing of SARS-CoV-2 transmission is a critical factor to understand the epidemic trajectory and the impact of isolation, contact tracing and other non-pharmaceutical interventions on the spread of COVID-19 epidemics. Methods: We examined the distribution of transmission event times with respect to exposure and onset of symptoms. We analysed 119 transmission pairs with known date of onset of symptoms for both index and secondary cases and partial information on their intervals of exposure. We inferred the distribution for generation time and time from onset of symptoms to transmission by maximum likelihood. We modelled different relations between time of infection, onset of symptoms and transmission, inferring the most appropriate one according to the Akaike Information Criterion. Finally, we estimated the fraction of pre-symptomatic and early symptomatic transmissions among all pairs using a Bayesian approach. Findings: For symptomatic individuals, the timing of transmission of SARS-CoV-2 was more directly linked to the onset of clinical symptoms of COVID-19 than to the time since infection. The time of transmission was approximately centered and symmetric around the onset of symptoms, with three quarters of events occurring in the window from 2-3 days before to 2-3 days after. The pre-symptomatic infectious period extended further back in time for individuals with longer incubation periods. Overall, the fraction of transmission from strictly pre-symptomatic infections was high (41%; 95%CI 31-50%), but a comparably large fraction of transmissions occurred on the same day as the onset of symptoms or the next day (35%; 95%CI 26-45%). We caution against overinterpretation of the fraction and timing of late symptomatic transmissions, due to their dependence on behavioural factors and interventions. Interpretation: Infectiousness is causally driven by the onset of symptoms. Public health authorities should reassess their policies on the contact tracing window in the light of individual variability in presymptomatic infectious period. Information about when a case was infected should be collected where possible, in order to assess how far into the past their contacts should be traced. The large fraction of transmission from strictly pre-symptomatic infections limits the efficacy of symptom-based interventions, while the large fraction of early symptomatic transmissions underlines the critical importance of individuals distancing themselves from others as soon as they notice any symptoms, even if mild. Rapid or at-home testing and contextual risk information could greatly facilitate efficient early isolation. Funding Statement: The study was funded by an award from the Li Ka Shing Foundation to CF. Declaration of Interests: None of the authors have competing financial or non-financial interests.

In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed points and stable periodic orbits, as well as regions of bistability. For arbitrary biologically feasible initial population sizes, the probability of evolving toward stable solutions is obtained for each point of the analyzed parameter space. This probability map shows combinations of infection rates of the generalist and specialist strains that might lead to equal chances for each type becoming the dominant strategy. Furthermore, we have identified infection rates for which the model predicts the onset of chaotic dynamics. Several degenerate Bogdanov–Takens and zero-Hopf bifurcations are detected along with generalized Hopf and zero-Hopf bifurcations. This manuscript provides additional insights into the dynamical complexity of host–pathogen evolution toward different infection strategies., A.N. received funding from the “La Caixa” Foundation and the Mathematics for Industry Network COST Action (No. TD1409). M.G.H. received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant (Agreement No. 707658). J.S. has been funded by a “Ramón y Cajal” Contract (No. RYC-2017-22243), and by the MINECO Grant (No. MTM2015-71509-C2-1-R) and the Spain’s “Agencia Estatal de Investigación” (AEI) Grant (No. RTI2018-098322-B-I00). L.A. has been supported by the AEI Grant (No. MTM2017-86795-C3-1-P). S.F.E.’s support comes from the AEI-FEDER Grant (No. BFU2015-65037-P) and Generalitat Valenciana Grant (No. PROMETEU/2019/012). The research leading to these results has received funding from the “la Caixa” Foundation, from a MINECO grant awarded to the Barcelona Graduate School of Mathematics (BGSMath) under the “María de Maeztu” Program (Grant No. MDM-2014-0445), and from the CERCA Programme of the Generalitat de Catalunya.