Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain

Key epidemiological drivers and impact of interventions in the 2020 SARS-CoV-2 epidemic in England

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Compared with other approaches, our model provides a synthesis of multiple surveillance data streams into a single coherent modelling framework allowing transmission and severity to be disentangled from features of the surveillance system. Of the control measures implemented, only national lockdown brought the reproduction number (Rteff ) below 1 consistently; if introduced one week earlier it could have reduced deaths in the first wave from an estimated 48,600 to 25,600 (95% credible interval [95%CrI]: 15,900-38,400). The infection fatality ratio decreased from 1.00% (95%CrI: 0.85%-1.21%) to 0.79% (95%CrI: 0.63%-0.99%), suggesting improved clinical care. The infection fatality ratio was higher in the elderly residing in care homes (23.3%, 95%CrI: 14.7%-35.2%) than those residing in the community (7.9%, 95%CrI: 5.9%-10.3%). On 2nd December 2020 England was still far from herd immunity, with regional cumulative infection incidence between 7.6% (95%CrI: 5.4%-10.2%) and 22.3% (95%CrI: 19.4%-25.4%) of the population. Therefore, any vaccination campaign will need to achieve high coverage and a high degree of protection in vaccinated individuals to allow non-pharmaceutical interventions to be lifted without a resurgence of transmission

Key epidemiological drivers and impact of interventions in the 2020 SARS-CoV-2 epidemic in England

We fitted a model of SARS-CoV-2 transmission in care homes and the community to regional surveillance data for England. Compared with other approaches, our model provides a synthesis of multiple surveillance data streams into a single coherent modelling framework allowing transmission and severity to be disentangled from features of the surveillance system. Of the control measures implemented, only national lockdown brought the reproduction number (Rteff ) below 1 consistently; if introduced one week earlier it could have reduced deaths in the first wave from an estimated 48,600 to 25,600 (95% credible interval [95%CrI]: 15,900-38,400). The infection fatality ratio decreased from 1.00% (95%CrI: 0.85%-1.21%) to 0.79% (95%CrI: 0.63%-0.99%), suggesting improved clinical care. The infection fatality ratio was higher in the elderly residing in care homes (23.3%, 95%CrI: 14.7%-35.2%) than those residing in the community (7.9%, 95%CrI: 5.9%-10.3%). On 2nd December 2020 England was still far from herd immunity, with regional cumulative infection incidence between 7.6% (95%CrI: 5.4%-10.2%) and 22.3% (95%CrI: 19.4%-25.4%) of the population. Therefore, any vaccination campaign will need to achieve high coverage and a high degree of protection in vaccinated individuals to allow non-pharmaceutical interventions to be lifted without a resurgence of transmission

Comparing the responses of the UK, Sweden and Denmark to COVID-19 using counterfactual modelling

The UK and Sweden have among the worst per-capita COVID-19 mortality in Europe. Sweden stands out for its greater reliance on voluntary, rather than mandatory, control measures. We explore how the timing and effectiveness of control measures in the UK, Sweden and Denmark shaped COVID-19 mortality in each country, using a counterfactual assessment: what would the impact have been, had each country adopted the others’ policies? Using a Bayesian semi-mechanistic model without prior assumptions on the mechanism or effectiveness of interventions, we estimate the time-varying reproduction number for the UK, Sweden and Denmark from daily mortality data. We use two approaches to evaluate counterfactuals which transpose the transmission profile from one country onto another, in each country’s first wave from 13th March (when stringent interventions began) until 1st July 2020. UK mortality would have approximately doubled had Swedish policy been adopted, while Swedish mortality would have more than halved had Sweden adopted UK or Danish strategies. Danish policies were most effective, although differences between the UK and Denmark were significant for one counterfactual approach only. Our analysis shows that small changes in the timing or effectiveness of interventions have disproportionately large effects on total mortality within a rapidly growing epidemic

Clinical history and management recommendations of the smooth muscle dysfunction syndrome due to ACTA2 arginine 179 alterations

Smooth muscle dysfunction syndrome (SMDS) due to heterozygous ACTA2 arginine 179 alterations is characterized by patent ductus arteriosus, vasculopathy (aneurysm and occlusive lesions), pulmonary arterial hypertension, and other complications in smooth muscle-dependent organs. We sought to define the clinical history of SMDS to develop recommendations for evaluation and management. Medical records of 33 patients with SMDS (median age 12 years) were abstracted and analyzed. All patients had congenital mydriasis and related pupillary abnormalities at birth and presented in infancy with a patent ductus arteriosus or aortopulmonary window. Patients had cerebrovascular disease characterized by small vessel disease (hyperintense periventricular white matter lesions; 95%), intracranial artery stenosis (77%), ischemic strokes (27%), and seizures (18%). Twelve (36%) patients had thoracic aortic aneurysm repair or dissection at median age of 14 years and aortic disease was fully penetrant by the age of 25 years. Three (9%) patients had axillary artery aneurysms complicated by thromboembolic episodes. Nine patients died between the ages of 0.5 and 32 years due to aortic, pulmonary, or stroke complications, or unknown causes. Based on these data, recommendations are provided for the surveillance and management of SMDS to help prevent early-onset life-threatening complications

Projected outcomes of universal testing and treatment in a generalised HIV epidemic in Zambia and South Africa (the HPTN 071 [PopART] trial): a modelling study

Background The long-term impact of universal home-based testing and treatment as part of universal testing and treatment (UTT) on HIV incidence is unknown. We made projections using a detailed individual-based model of the effect of the intervention delivered in the HPTN 071 (PopART) cluster-randomised trial. Methods In this modelling study, we fitted an individual-based model to the HIV epidemic and HIV care cascade in 21 high prevalence communities in Zambia and South Africa that were part of the PopART cluster-randomised trial (intervention period Nov 1, 2013, to Dec 31, 2017). The model represents coverage of home-based testing and counselling by age and sex, delivered as part of the trial, antiretroviral therapy (ART) uptake, and any changes in national guidelines on ART eligibility. In PopART, communities were randomly assigned to one of three arms: arm A received the full PopART intervention for all individuals who tested positive for HIV, arm B received the intervention with ART provided in accordance with national guidelines, and arm C received standard of care. We fitted the model to trial data twice using Approximate Bayesian Computation, once before data unblinding and then again after data unblinding. We compared projections of intervention impact with observed effects, and for four different scenarios of UTT up to Jan 1, 2030 in the study communities. Findings Compared with standard of care, a 51% (95% credible interval 40–60) reduction in HIV incidence is projected if the trial intervention (arms A and B combined) is continued from 2020 to 2030, over and above a declining trend in HIV incidence under standard of care. Interpretation A widespread and continued commitment to UTT via home-based testing and counselling can have a substantial effect on HIV incidence in high prevalence communities. Funding National Institute of Allergy and Infectious Diseases, US President's Emergency Plan for AIDS Relief, International Initiative for Impact Evaluation, Bill & Melinda Gates Foundation, National Institute on Drug Abuse, and National Institute of Mental Health

Establishment and cryptic transmission of Zika virus in Brazil and the Americas

Transmission of Zika virus (ZIKV) in the Americas was first confirmed in May 2015 in northeast Brazil1. Brazil has had the highest number of reported ZIKV cases worldwide (more than 200,000 by 24 December 20162) and the most cases associated with microcephaly and other birth defects (2,366 confirmed by 31 December 20162). Since the initial detection of ZIKV in Brazil, more than 45 countries in the Americas have reported local ZIKV transmission, with 24 of these reporting severe ZIKV-associated disease3. However, the origin and epidemic history of ZIKV in Brazil and the Americas remain poorly understood, despite the value of this information for interpreting observed trends in reported microcephaly. Here we address this issue by generating 54 complete or partial ZIKV genomes, mostly from Brazil, and reporting data generated by a mobile genomics laboratory that travelled across northeast Brazil in 2016. One sequence represents the earliest confirmed ZIKV infection in Brazil. Analyses of viral genomes with ecological and epidemiological data yield an estimate that ZIKV was present in northeast Brazil by February 2014 and is likely to have disseminated from there, nationally and internationally, before the first detection of ZIKV in the Americas. Estimated dates for the international spread of ZIKV from Brazil indicate the duration of pre-detection cryptic transmission in recipient regions. The role of northeast Brazil in the establishment of ZIKV in the Americas is further supported by geographic analysis of ZIKV transmission potential and by estimates of the basic reproduction number of the virus