key: cord-266070-28a85p50
authors: Oberhammer, J.
title: Social-distancing effectiveness tracking of the COVID-19 hotspot Stockholm
date: 2020-07-02
journal: nan
DOI: 10.1101/2020.06.30.20143487
sha: 
doc_id: 266070
cord_uid: 28a85p50

Background: The COVID-19 outbreak in Stockholm, Sweden, is characterized by a near-absence of governmental interventions and high fatalities in the care home population. This study analyses the outbreak and the social-distancing effectiveness timeline in the general population and the care homes. Methods: A novel distributed-compartmental, time-variant epidemiological model was designed specifically for COVID-19 transmission characteristics, featuring a/pre/symptomatic transmission, a non-linear hospital model, a weakly-coupled sub-model for the care-home population, and parametrized continuous social-distancing functions. The model parameters and the social-distancing timelines are determined by randomization and Monte-Carlo simulations analysing real-world data. Findings: Despite a high initial reproduction number (3.29) and the near-absence of governmental interventions, the model quantitated that the transmission rate in the general population was suppressed by 73%, and in the care homes by 79%. The measures in the care homes took effect 4.8 days delayed; and if applied 4 or 8 days earlier, the fatalities could have been reduced by 63.2% or 89.9%. The infected population is estimated to 16.2% (June 10). An expected underestimation of population immunity by antibody studies is confirmed. The infection fatality ratio extrapolates to 0.61% (peak: 1.34%). The model indicates a seasonal effect which effectively suppressed a new rise. An analysed large-scale public event had no large influence. The asymptomatic ratio was determined to 35%. Interpretation: The proposed model and methods have proven to analyse a COVID-19 outbreak and to re-construct the social-distancing behaviour with unprecedented accuracy, confirming even minor details indicated by mobility-data analysis, and are applicable to other regions and other emerging infectious diseases of similar transmission characteristics. The self-regulation of the population in Stockholm, influenced by advices by the authorities, was able to suppress a COVID-19 outbreak to a level far beyond that the stringency index of governmental interventions suggests. Proper timing of effective measures in the care homes is important to reduce fatalities.

Background The COVID-19 outbreak in Stockholm, Sweden, is characterized by a near-absence of 25 governmental interventions and high fatalities in the care home population. This study analyses the 26 outbreak and the social-distancing effectiveness timeline in the general population and the care 27 homes. 28

Methods A novel distributed-compartmental, time-variant epidemiological model was designed 29 specifically for COVID-19 transmission characteristics, featuring a/pre/symptomatic transmission, a 30 non-linear hospital model, a weakly-coupled sub-model for the care-home population, and 31

parametrized continuous social-distancing functions. The model parameters and the social-32 distancing timelines are determined by randomization and Monte-Carlo simulations analysing real- 33 world data. 34

Findings Despite a high initial reproduction number (3·29) and the near-absence of governmental 35 interventions, the model quantitated that the transmission rate in the general population was 36 suppressed by 73%, and in the care homes by 79%. The measures in the care homes took effect 4·8 37 days delayed; and if applied 4 or 8 days earlier, the fatalities could have been reduced by 63·2% or 38

89·9%. The infected population is estimated to 16·2% (June 10). An expected underestimation of 39 population immunity by antibody studies is confirmed. The infection fatality ratio extrapolates to 40 0·61% (peak: 1·34%). The model indicates a seasonal effect which effectively suppressed a new rise. 41 An analysed large-scale public event had no large influence. The asymptomatic ratio was determined 42

to 35%. 43 Interpretation The proposed model and methods have proven to analyse a COVID-19 outbreak and 44

to re-construct the social-distancing behaviour with unprecedented accuracy, confirming even minor 45 details indicated by mobility-data analysis, and are applicable to other regions and other emerging 46 infectious diseases of similar transmission characteristics. The self-regulation of the population in 47

Stockholm, influenced by advices by the authorities, was able to suppress a COVID-19 outbreak to a 48 level far beyond that the stringency index of governmental interventions suggests. Proper timing of 49 effective measures in the care homes is important to reduce fatalities. 50 51 52 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 2, 2020. Modelling is also used to determine key parameters such as population immunity and infection 67 fatality rate (IFR), and to analyse the impact of imposing and revoking social-distancing 68 measures. 6, 7, 8, 9, 10 A well-established class of models is the Susceptible(S)-Exposed(E)-Infected(I)-69

Recovered(R)-Deceased(D) compartmental model. 11, 12, 13 Due to short simulation times, in particular 70 deterministic SEIRD models are used for parameter estimation by randomization. 14 (1) 92 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 2, 2020. ( )). Transmission-events feedback from the CH to the GP model is assumed neligible. 104

The hospital model comprises a primary ward, an intensive care, and a secondary general-ward 105 compartment for severely-sick, critically-sick, and patients recovering from intensive care, 106

respectively. 107

The GP and CH transmission rates are scaled by the time-variant factors 0 and , in the following 109 referred to as social-distancing effectiveness functions (SDEF), which track the social-distancing 110 behaviour and seasonal effects. All elements of the transmission-rate matrix are independently 111 controllable by time-dependent reduction factors, which allows to investigate the effect of different 112

advices to the population, from staying-home with symptoms to whole-household quarantine 113 (Figure 2 :B). 114

Since the reported number of patients in ICU in Stockholm follows not exactly the shape of the 115 general ward, it was assumed that with time a growing proportion of patients can be kept in regular 116 ward, which was implemented by a three-parameter logistics function (details in Appendix). The 117

hospital death rate, in relation to the hospital occupancy, was found to decrease with time, which 118 might reflect increasing treatment experience or a reduced number of CH patients transferred to 119 hospital, which is also modelled by a parametrized logistics function. A non-linear hospital and ICU 120 death-rate scaling factor, depending on the hospital occupancy, is also implemented by a logistics 121 function. 122

The onset of symptoms after infection is set to 5 days (discretization of the 5·2 days incubation 124 time). 22, 23 The distribution of the transmission rates in the two presymptomatic (I1, I2) and the two 125 symptomatic (I3, I4) infectious compartments (Figure 2 :A) is following the distribution of 126

transmission-pair analysis so that the proportion of the presymptomatic transmission events in the 127 symptomatic branch is 44%. 24 The total contagious period (I1-I4) is 7 day. 22 Since literature reports no 128 significant difference in viral spread between asymptomatic and symptomatic individuals, 25,26 the 129 initial infectivity in the two branches is the same, followed by a 75% reduction after the first 130 symptomatic day in the symptomatic branch when symptomatic individuals are assumed to reduce 131 social interaction. 132

The proportion of cases moving into the asymptomatic branch is determined by analysing the 133 proportion of non-symptomatic (asymptomatic and presymptomatic) individuals testing PCR-134 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. repatriating individuals to the UK; 2 average: 41·5%; Figure 3 ). The best matching asymptomatic-137 branch proportion is 35%, assuming that Reff in the studies is around 1·0. 138

Antibody development in the model is assumed to happens within 1 to 3 weeks after infection 29 ICU: 2·1 days). 32 The average times on regular (H1) and on post-ICU (H2) ward are 8 and 5 days, 150

respectively. 33 It is assumed that most people surviving ICU recover, therefore the H2 death rate is 151 arbitrarily set to 5% of the H1 death rate. The hospitalization-rate distribution, i.e. the transfer from 152 the GP symptomatic-branch compartments, was set so that the average time from onset of 153 symptoms to hospitalization is 8·16 days. 32 154

Model fitting to real-world data: social-distancing tracking 155

The starting values and randomization confidence intervals of the unknown model parameters (SDEF 156 for GP and CH; hospitalization rate; ward-to-ICU transfer, hospital death-rate, and the hospital non-157 linearity parameters) were determined by sensitivity analysis using multi-dimensional parameter 158 variation, with the GP SDEF initially modelled by a three-parameter logistics function. The 159 parameters were then refined by randomization with Monte-Carlo simulations. Minimum mean 160 square error functions were used to benchmark the model outcome to real-world data: the number 161 of patients in critical care and in intensive care, the number of date-adjusted GP and CH deaths 162 (daily situation reports, Region Stockholm), and the results of two PCR studies by FHM in April. 34,35 163 The results of four weekly antibody studies by FHM (April to June), 36 where non-COVID-19 patients 164 seeking ambulatory care in Stockholm were sampled, was not included for model fitting since FHM 165

reported on May 26 a potential bias towards persons with a lower risk of infection for this type of 166 sampling, and since in particular mild/asymptomatic people do not have a robust antibody 167 response. 26,37 168 The model is started by injecting infected cases to the latency compartment so that the daily new 169

infections are matching the reported confirmed cases from contact tracing, assuming a 5-day 170 reporting delay and a 5-10 times larger dark number range (Figure 3:B) . The injections happen 171 primarily in Stockholm's winter school vacation week, reported by FHM to have been the major 172 source of imported cases. 173

For the determination of the SDEF function of the GP by Monte-Carlo simulations, 15 randomized 174 points with shape-preserving piecewise cubic interpolation were mapped on the initial logistics 175

function. The points were optimized by three subsequent Monte-Carlo batches with 1 million 176 simulation runs each, where the 95%CI calculated from the corrected sample standard deviation of 177 the 100 best functions of a previous batch were used as the 95%CI for the randomization in a 178 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. . https://doi.org/10.1101/2020.06.30.20143487 doi: medRxiv preprint Joachim Oberhammer, KTH Royal Institute of Technology, 2020-06-25 subsequent batch (convergence shown in Figure 4 :A). The optimization of the hospital parameters 179 was done by a subsequent 1-million-run batch (Figure 4:C) . For the CH model, the SDEF was 180 modelled as a three-parameter logistic function, determined with the internal and external 181 transmission-rate factors by a 1-million simulation-run batch. All parameters were fine-adjusted with 182 a combined 1-million run batch. More details on the model and data fitting in the Appendix. 183 184

The SDEF determined for the GP with the advices to the population by FHM, governmental 187 measures, and key events of the outbreak mapped on the timeline, with comparison to Google's 188 mobility data analysis 38 and the Oxford Governmental Stringency Index, 15 is shown in Figure 5 . From 189 an initial 1·0 (February 1), the function falls to a minimum of 0·29 (April 5). The major reduction 190 happens between March 6 and 20, when the majority of the governmental restrictions and advices 191

were issued. The slope and the increase after April 4 are in good agreement with the mobility data, 192

which recorded for Stockholm a major slope between March 7 and March 19 (-31% retail/recreation 193 mobility; -45% public-transport; -42% workplace-mobility) and shows a minimum for the Easter 194

weekend, for which media reported a traffic reduction by 90% as compared to previous years. A 195 more detailed mapping of the Easter week (April 5-15) was carried out by three additional 196 randomization points, while randomizing also all surrounding and following points in two 1-million 197 simulation-run batches (Figure 4:B) , revealing a 3·9% improved error-function, a deeper SDEF 198 minima to 0·27, and a rise thereafter to the previous level (comparison of the two SDEF in Figure 5 ). 199

After Figure 6 summarizes the model results, showing an excellent fit to the real-world data 220

( ̅ 2 =0·9890/0·9886/0·9995/0·9986; internally-studentized residuals shown). The basic reproduction 221 number R0 was determined to 3·29, by replacing the starting sequence with an equivalent single 222 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. and to quantitate the social-distancing effectiveness function with an unprecedented accuracy so 258 that even small details in the timeline, indicated by mobility data analysis, were resolved. The model 259

is constructed as a trade-off between model complexity, accuracy, and speed for suitability for large-260 scale data fitting methods. This study has quantitated that by primarily relying on the advices by 261 authorities and on the self-regulation of the population, as in Sweden, it is possible to at least 262 temporarily suppress COVID-19 by 73%, far beyond the government stringency-index indication. The 263

determined social-distancing behaviour of the general population follows the mobility data analysis, 264

whereas the determined care homes transmission-rate reduction, delayed by several days, follows 265 the delayed government stringency index timeline. This indicates that the general-population self-266 regulation effect was ahead of time of the effect of governmental measures. The decrease of the 267 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. function. An anticipated underestimation of the population immunity by antibody studies is 271

confirmed. This study has quantitated the importance of applying early care-home protection 272

measures. The analysis of Europe's last large-scale public event in pre-corona times has found that at 273 an already wide-spread community transmission such an event has a significantly lower impact as 274 compared to happening in a more sensitive earlier phase. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 2, 2020. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 2, 2020. . https://doi.org/10.1101/2020.06.30.20143487 doi: medRxiv preprint Monte-Carlo simulations data-fitting, with advices and governmental restrictions mapped on the 318 timeline (A=advice by Public Health Agency; GR=governmental restriction; CR=care-home 319 restriction), including a SDEF variation with additional randomization points for resolving the Easter 320

week minima indicated by the mobility data; middle: Google mobility data for Stockholm; 38 bottom: 321

Oxford government stringency index for Sweden. 15 322 323 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 2, 2020. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 2, 2020. . https://doi.org/10.1101/2020.06.30.20143487 doi: medRxiv preprint

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