Modelling the impact of local reactive school closures on critical care provision during an influenza pandemic: Supplementary Material Thomas House 1,*, Marc Baguelin 2,6, Albert Jan van Hoek 2, Peter J. White 3,4, Zia Sadique 5, Ken Eames 6, Jonathan M. Read 7, Niel Hens 8,9, Alessia Melegaro 1, W. John Edmunds 2,6, and Matt J. Keeling 1,11 1 Warwick Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK. 2 Immunisation Department, Health Protection Agency, 61 Colindale Avenue, London, NW9 5EQ, UK. 3 Modelling and Economics Unit, Health Protection Agency, 61 Colindale Avenue, London, NW9 5EQ, UK. 4 MRC Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College Faculty of Medicine, Norfolk Place, London, W2 1PG, UK. 5 Health Services Research Unit, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. 6 Infectious Diseases Epidemiology Unit, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. 7 Institute of Infection and Global Health, University of Liverpool, Leahurst campus, Neston, CH64 7TE, UK. 8 Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1, B359 Diepenbeek, Belgium. 9 Centre for Health Economics Research and Modeling Infectious Diseases and Centre for the Evaluation of Vaccination, Vaccine and Infectious Disease Institute, University of Antwerp, Belgium. 1 DONDENA Centre for Research on Social Dynamics, Bocconi University, Via Guglielmo Röntgen n.1, 2136 Milan, Italy. 11 Department of Biological Sciences, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK. * Corresponding Author: T.A.House@warwick.ac.uk We present here information that allows reproduction of our results, details the models used and assesses the sensitivity and validation of our assumptions. 1
1 Geographical considerations We consider some of the geographical aspects relevant to this work, particularly in Figure S1 below. To demonstrate intuitively the complexities involved at a local scale, we show a typical area around a hospital in Panel (c). In this figure, the hospital location is shown as a grey marker, surrounded by the convex hull around its catchment. Movements from pupil home locations to school locations are shown as lines coloured by school; these are extremely dense within the (approximate) catchment region and extend a significant distance outside it, demonstrating the complex structure of interactions even at a local scale. Panel (a) shows the distances associated with work movement of adults (recorded at Output Area level in the 21 UK census), together with age-stratified movements to school recorded at LSOA level for schoolage children in the 27 Spring School census. Clearly the majority of all movements occur within a 1km radius of the home. Panel (b) shows the typical distances associated with primary and secondary schools, based on mean school school distances. These are primarily included for general interest, and to help with intuitive understanding of results. 2 Sensitivity analysis Underlying the plots in the main paper is a number of local schools that is turned into a percentage of English schools. We present our sensitivity results in terms of this number to make it easier to see the size of each effect considered. 2.1 Interaction between local areas Our baseline model for the impact of school closures assumes a linear relationship between the proportion of a hospital catchment population affected by school closure and the reduction in peak demand for adult ICU. Model results relevant for sensitivity to this assumption are shown in Figure S2. The schematic representation of this model is shown in Panel (a), where we assume that a fraction 1 ε of all adult interactions occur within the closure region, with the remainder occurring outside. Shown in blueε G is the simplest assumption that these external interactions are to outside the hospital catchment area and have no dynamical impact on the external population. The alternative assumption (shown in redε L ) is that all of the interactions are within the hospital catchment area, and therefore have a dynamical impact on the total peak within that region. It is worth noting that a smaller fraction of school closures within the hospital catchment area necessitates a later closure to achieve the maximum impact on the total peak. We then translate this into a non-linear response of the epidemic peak to school closure proportion p in Panels (b) and (c). We see that for global coupling, our baseline linear assumption is justified, but for local coupling the non-linearity is significant. In addition, some non-monotonicity is seen due to counterintuitive effects that arise from optimal timing generating two peaks. Since some coupling will be local and some global, the magenta line in Panel (b) will be an overestimate of non-linearity, and this line leads to the variation shown in Panels (d) and (e) as regions around the baseline lines. 2.2 Correlated heterogeneity in catchments We also consider the validity of assumptions made in our model about hospital catchments. One assumption was to ignore the dynamical effects of heterogeneity in age profiles between hospital catchment areas. The results of relaxing this assumption are shown in Figure S3. There is modest heterogeneity in the number of children in each catchment (Panel (a)) and this quantity is inversely correlated with the ICU capacity per adult (Panel (b)). If this is turned into a correlation between demand and capacity in each catchment, as at least a rough estimate of this effect, then the variability in results is shown in Panels (c) and (d). 2.3 Hospital catchments Another assumption tested here is that individuals move to their nearest hospital in the first instance. We can test the potential impact of alternative protocols by assuming that the movement of individuals minimises the quantity Distance (Total Beds) α, 2
and then finding a value forαthat minimises the number of adults over capacity in the absence of school closures, with results shown in Figure S4. Optimal values ofαare shown in Panel (a), while Panels (b) and (c) show how the main results change on the basis of the optimised catchments. 3 Sources of data Our work draws on a large number of data sources, which we detail below: Digital boundary data Source: 21 Census, Output Area Boundaries. Crown copyright 23. Office for National Statistics, 21 Census: Digitised Boundary Data (England and Wales) [computer file]. ESRC/JISC Census Programme, Census Geography Data Unit (UKBORDERS), EDINA (University of Edinburgh). General Register Office for Scotland, 21 Census: Digitised Boundary Data (Scotland) [computer file]. ESRC/JISC Census Programme, Census Geography Data Unit (UKBORDERS), EDINA (University of Edinburgh). Census output is Crown copyright and is reproduced with the permission of the Controller of HMSO and the Queen s Printer for Scotland. Super Output Area boundaries Source: Office for National Statistics, Super Output Area Boundaries. Crown copyright 24. Crown copyright material is reproduced with the permission of the Controller of HMSO. Super Output Area lookup tables Source: Office for National Statistics, Neighbourhood Statistics DVD- ROM V1.3 (April 25). Super Output Area populations Source: Office for National Statistics, Mid-27 Population Estimates for Lower Layer Super Output Areas in England and Wales by Broad Age Group and Sex. Crown copyright 28. Hospital Capacity Source: Department of Health form KH3a, Open and staffed adult critical care beds at 15 January 29, by location and level of care, NHS Trusts in England. Published 27 February 29. Hospital Locations Source: www.nhs.uk/servicedirectories/pages/acutetrustlisting.aspx (Accessed December 13, 21). Geographical lookup Provided by GeoConvert: geoconvert.mimas.ac.uk (Accessed December 13, 21). School data Source: Department for Children, Schools and Families, PLASC/Census 26/27 Spring data. Interaction data Source: 21 Census: Special Workplace Statistics (England, Wales and Northern Ireland). Office for National Statistics, 21 Census: Special Workplace Statistics (England, Wales and Northern Ireland) [computer file]. ESRC/JISC Census Programme, Centre for Interaction Data Estimation and Research (University of Leeds). Census output is Crown copyright and is reproduced with the permission of the Controller of HMSO and the Queen s Printer for Scotland. H1N1 dynamical model Sources: Baguelin et al. (21); Hens et al. (29); Mossong et al. (28). References Marc Baguelin, Albert Jan Van Hoek, Mark Jit, Stefan Flasche, Peter J White, and W John Edmunds. Vaccination against pandemic influenza A/H1N1v in England: A real-time economic evaluation. Vaccine, 28(12):237 2384, Mar 21. Niel Hens, Girma Minalu Ayele, Nele Goeyvaerts, Marc Aerts, Joël Mossong, W John Edmunds, and Philippe Beutels. Estimating the impact of school closure on social mixing behaviour and the transmission of close contact infections in eight european countries. BMC Infectious Diseases, 9:187, November 29. Joël Mossong, Niel Hens, Mark Jit, Philippe Beutels, Kari Auranen, Rafael Mikolajczyk, Marco Massari, Stefania Salmaso, Gianpaolo Scalia Tomba, Jacco Wallinga, Janneke Heijne, Malgorzata Sadkowska- Todys, Magdalena Rosinska, and W. John Edmunds. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med, 5(3):381 391, Jan 28. 3
Supplementary figures Proportion travelling over distance to school / work 1.8.6.4.2 Age 4 Age 5 Age 6 Age 7 Age 8 Age 9 Age 1 Age 11 Age 12 Age 13 Age 14 Age 15 Age 16 Age 17 Age 18 Age > 18 Adult Workers 1 5 1 4 1 3 N 1 2 1 1 Primary Schools Secondary Schools 1 1 1 1 1 1 2 Distance (km) (a) Distance kernels 1 1 1 1 1 1 1 2 Mean distance to N th school (km) (b) School spatial separation (c) A typical area Figure S1: Geographical considerations. (a) scale of commuter movements, school movements. (b) school locations. (c) shows a typical hospital as a grey circle with a black border. The convex hull around the population-weighted centroids of LSOAs in the catchment area is shown as a black line, to avoid problems of identifiability with exact boundaries. Links between pupil home and school, granulated at the level of LSOA centroids, are shown as lines coloured by school. 4
(a) Schematic of model % of p=1 demand reduction 1 8 6 4 2.2.4.6.8 1 Proportion of Schools Closed, p.8.6.4.2 Local Coupling, ε L (b) Non-linearity of response to p givenε L, interactions within the catchment % of p=1 demand reduction 1 8 6 4 2.2.4.6.8 1 Proportion of Schools Closed, p.9.8.7.6.5.4.3.2.1 Global Coupling, ε G (c) Non-linearity of response to p givenε G, interactions outside the catchment Maximum adults over ICU capacity 25 2 15 1 5 5 1 15 2 (d) Sensitivity to non-linearity Percentage of hospitals over adult ICU capacity 1 8 6 4 2 5 1 15 2 (e) Sensitivity to non-linearity Figure S2: (a) shows a schematic of the model used to test linearity of response to school closure a hospital H has a catchment (light grey region) with a fraction p of that catchment subject to school closure. We then let a fraction of adults interacts with either the remainder of the hospital catchment (ε L ) or the rest of England (ε G ). (b) and (c) show coupled-patch model results on the non-linearity of response to school closure, while (d) and (e) are model sensitivity to these effects. 5
Number of catchments 4 35 3 25 2 15 1 5 12 13 14 15 16 17 18 19 2 21 22 23 24 25 % children in catchment (a) Histogram of percentage of catchment population that is children Number of adult ICU beds 1 8 6 4 2 r 2 5% r 2 17% 12 13 14 15 16 17 18 19 2 21 22 23 24 25 % children in catchment (b) Percentage of catchment that is children against absolute and proportional adult ICU capacity 1.8.6.4.2 Adult ICU beds per 1 adults Maximum adults over ICU capacity 25 2 15 1 5 5 1 15 2 (c) Correlated demand and supply Percentage of hospitals over adult ICU capacity 1 8 6 4 2 5 1 15 2 (d) Correlated demand and supply Figure S3: (a) heterogeneity in hospital catchment age distribution, and (b) how this correlates inversely with capacity together with r 2 values. (c) and (d) show model sensitivity to correlation between demand for ICU and capacity. 6
Number of adults 25 2 15 1 5 Peak at 1% Peak at 67% Peak at 15% 1% peak optimum 67% peak optimum 15% peak optimum.2.4.6.8 1 α (a) Optimal α values Maximum adults over ICU capacity 25 2 15 1 5 5 1 15 2 (b) Optimal hospital catchment Percentage of hospitals over adult ICU capacity 1 8 6 4 2 5 1 15 2 (c) Optimal hospital catchment Figure S4: Sensitivity to modification hospital catchments by allocating LSOAs to hospitals on the basis of minimising distance/beds α (baselineα=) then optimisingα to minimise the number of adults per adult ICU bed in the catchment. (a) shows optimal α values while (b) and (c) show the baseline results together with shaded regions representing sensitivity to this effect. 7