Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID- 19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. G Model GACETA-1867; No. of Pages 6 ARTICLE IN PRESS Gac Sanit. 2020;xxx(xx):xxx–xxx Original Analysis of the impact of lockdown on the reproduction number of the SARS-Cov-2 in Spain Alexandre Hyafila,b,∗ , David Moriñab,c a Centre de Recerca Matemàtica, Edifici C, Universitat Autònoma de Barcelona, Cerdanyola del Vallès (Barcelona), Spain b Barcelona Graduate School of Mathematics, Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès (Barcelona), Spain c Department of Econometrics, Statistics and Applied Economics, Riskcenter-IREA, Universitat de Barcelona, Barcelona, Spain a r t i c l e i n f o a b s t r a c t Article history: Objective: The late 2019 COVID-19 outbreak has put the health systems of many countries to the limit Received 18 April 2020 of their capacity. The most affected European countries are, so far, Italy and Spain. In both countries Accepted 6 May 2020 (and others), the authorities decreed a lockdown, with local specificities. The objective of this work is to Available online xxx evaluate the impact of the measures undertaken in Spain to deal with the pandemic. Method: We estimated the number of cases and the impact of lockdown on the reproducibility number Keywords: based on the hospitalization reports up to April 15th 2020. COVID-19 Results: The estimated number of cases shows a sharp increase until the lockdown, followed by a slowing Evaluation study Public health down and then a decrease after full quarantine was implemented. Differences in the basic reproduction Infections ratio are also significant, dropping from 5.89 (95% confidence interval [95%CI]: 5.46-7.09) before the Virus lockdown to 0.48 (95%CI: 0.15-1.17) afterwards. Conclusions: Handling a pandemic like COVID-19 is complex and requires quick decision making. The large differences found in the speed of propagation of the disease show us that being able to implement interventions at the earliest stage is crucial to minimise the impact of a potential infectious threat. Our work also stresses the importance of reliable up to date epidemiological data in order to accurately assess the impact of Public Health policies on viral outbreak. © 2020 SESPAS. Published by Elsevier España, S.L.U. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Análisis del impacto del confinamiento en el número de reproducción del SARS-Cov-2 en España r e s u m e n Palabras clave: Objetivo: El brote de COVID-19 a finales de 2019 ha puesto los sistemas de salud de muchos países al COVID-19 límite de su capacidad. Los países europeos más afectados son, hasta ahora, Italia y España. En ambos (y Estudio de evaluación en otros países), las autoridades decretaron un confinamiento, con especificidades locales. El objetivo de Salud pública este trabajo es evaluar el impacto de las medidas adoptadas en España para hacer frente a la pandemia. Infecciones Método: Estimamos el número de casos y el impacto del confinamiento en el número básico de repro- Virus ducción según los informes de hospitalización hasta el 15 de abril de 2020. Resultados: El número estimado de casos muestra un fuerte aumento hasta el bloqueo, seguido de una desaceleración y luego una disminución tras la implementación del confinamiento total. Las diferencias en el número básico de reproducción también son muy significativas, cayendo de 5,89 (intervalo de confianza del 95% [IC95%]: 5,46-7,09) antes del bloqueo a 0,48 (IC95%: 0,15-1,17) después. Conclusiones: Gestionar una pandemia como la de COVID-19 es muy complejo y requiere una rápida toma de decisiones. Las grandes diferencias encontradas en la velocidad de propagación de la enfermedad muestran que poder implementar intervenciones en la etapa más temprana es crucial para minimizar el impacto de una potencial amenaza. Nuestro trabajo también indica la importancia de contar con datos epidemiológicos actualizados y confiables para evaluar con precisión el impacto de las políticas de salud pública en la pandemia. © 2020 SESPAS. Publicado por Elsevier España, S.L.U. Este es un artı́culo Open Access bajo la licencia CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/). Introduction By late 2019 an outbreak of COVID-19, caused by SARS-Cov- 2 virus, started in the region of Hubei (China), more specifically ∗ Corresponding author. in the city of Wuhan. Since then, the disease has spread all E-mail address: ahyafil@crm.cat (A. Hyafil). over the world, being declared pandemic by the World Health https://doi.org/10.1016/j.gaceta.2020.05.003 0213-9111/© 2020 SESPAS. Published by Elsevier España, S.L.U. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc- nd/4.0/). Please cite this article in press as: Hyafil A, Moriña D. Analysis of the impact of lockdown on the reproduction number of the SARS-Cov-2 in Spain. Gac Sanit. 2020. https://doi.org/10.1016/j.gaceta.2020.05.003 G Model GACETA-1867; No. of Pages 6 ARTICLE IN PRESS 2 A. Hyafil, D. Moriña / Gac Sanit. 2020;xxx(xx):xxx–xxx 0.14 Detection 0.12 Hospitalization Death 0.1 Probability of evet 0.08 0.06 0.04 0.02 0 0 5 10 15 20 25 30 35 40 45 Days after contamination Figure 1. Normalized distribution for the latency from contamination to detected case, hospitalization and death event. Organization on 2020 March 11th. The rapid propagation of the distancing measures (no measure, state emergency or mandatory virus around the world has stressed the health systems of many confinement). Those three expected values are parameters that are countries to their limit. In Europe, the most affected countries in estimated from the reports. Formally, the priors over R0 for each terms of number of detected cases, hospitalizations and deaths are, region are defined as independent Gaussian processes. The prior to the date, Italy and Spain. This unprecedented situation for the mean is defined by the distancing measures, while the prior covari- public health systems of these countries forced decision makers ance is squared exponential covariance K with variance  2 = 0.12 to act very quickly in order to minimize the impact of the disease and length l = 1 day.6 Such prior allows to capture differences in and to avoid collapse. In Spain, the emergency state was declared the spread between different regions as well as temporary change on 2020 March 14th and was hardened with mandatory home of R0 within a region (Gaussian processes enforce that these fluc- confinement except for vital sectors workers (including health pro- tuations are smooth in time). The variance term  2 was set so it is fessionals, food supply, etc.) on March 30th. Under this situation, unlikely that the infected population goes down in a single day by it is urgent to assess the efficiency of social distancing and other a proportion larger than the recovery rate . Based on the mean 20 non-pharmaceutical interventions undertaken to control the pan- days of contagious before recovery (duration of viral shedding7 ), we demics of COVID-19.1,2 One of the main challenges in evaluating set  = 0.05day−1 . We assumed that the value of infected people the impact of these actions is that data are only partially available, at the beginning of the period studied (20th of February 2020) was as many of the cases are asymptomatic or with mild symptoms,3 drawn from a log-normal distribution with mean xi (r) and variance and shortage of testing kits prevent testing all patients with pos- 1, where xi is a parameter specific to each autonomous community sible COVID-19 symptoms. Therefore, the number of cases might (estimated from the data). This variability allowed us to capture be severely underestimated. This issue is common in epidemiol- initial variations in the spread of the epidemics at the beginning of ogy and several methods have been recently proposed to address the period of study. it under specific circumstances.4,5 Another issue is that, when no The number of new cases per day is N (r, d) = I (r, d) − massive viral testing of the population is performed, new cases I (r, d − 1) + I (r, d − 1) = I (r, d) − (1 − ) I (r, d − 1). This true are only detected once symptoms appear, at a variable delay after number of cases however cannot be observed directly. Here contamination. This complicates the assessment of the impact of we use a latent-state approach: we estimated the evolution interventions to reduce/slow down the spread of a virus. of the number of true cases in each autonomous community Here, we aimed at evaluating the impact of the COVID-19 based on the recorded accumulated number of detected cases, related non-pharmaceutical interventions undertaken in Spain hospitalizations and deaths provided by Instituto de Salud Carlos over the basic reproduction ratio R0 , considering three periods III7 . We used estimates for the proportion of cases pC that are of time in 2020: no intervention (until March 13th), emergency detected by the Spanish Health system, the proportion of cases state (March 16-30th and April 13th-15th) and mandatory con- pH that are hospitalized, and the lethality rate pD , as the well as finement (March 31st to April 12th). We inferred retrospectively the distribution of latency between infection and this three types the number of contamination in each Spanish autonomous com- of events li (d) (Fig. 1). We used the following estimates: 15% of munity from the patterns of hospitalizations, deaths and detected contaminated persons are hospitalized; 1% die from disease8,9 ; 30% cases. Analyses were performed with data up to April 15th 2020. of cases get detected (this latter number was defined arbitrarily, since the number of detected cases is roughly twice the number of Methods hospitalizations). Note that these percentages affect the estimated number of true cases by a scaling factor, but do not affect the We modelled the dynamics of infection with a discrete-time estimation of reproduction parameters. We used estimates of SIR (Susceptible-Infected-Recovered) model with time-varying R0 the distribution of duration of infection-to-detection, infection- defined for each region r and day d. We also assumed the stock of to-hospitalization based on published literature.8,9 Lauer and susceptible population S (r, d) is almost constant through time at colleagues describe that the incubation period can be cap- S (r, d) ≈ Nr , (where Nr is the size of the total population in the tured by log-normal distribution with median 5.1 days. To region; i.e. a small percentage of the population is contaminated) capture the extra time from the apparition of symptoms to case as is probably valid up to now. The dynamics of infected people detection/hospitalization, we increased the median time of the I (r, d) an region r at day d thus varies as: log-normal distribution by 50% for case detection and 100% for hospitalization, i.e. 7.65 days and 10.2 days, respectively, while I (r, d + 1) = I (r, d) e(R0 (r,d)−1) , (1) keeping the same dispersion parameter . For infection-to-death, where  is the recovery rate of the infection and R0 is a stochas- we used the sum of two gamma distributions for infection-to- tic variable whose expected value is defined by the ongoing social onset and onset-to-death with overall mean 23.9 days.10 Thus Please cite this article in press as: Hyafil A, Moriña D. Analysis of the impact of lockdown on the reproduction number of the SARS-Cov-2 in Spain. Gac Sanit. 2020. https://doi.org/10.1016/j.gaceta.2020.05.003 G Model GACETA-1867; No. of Pages 6 ARTICLE IN PRESS A. Hyafil, D. Moriña / Gac Sanit. 2020;xxx(xx):xxx–xxx 3 106 105 Number of patients 104 Estimated cases Detected cases 103 Hospitalizations Deaths 102 Feb 19 Feb 26 Mar 04 Mar 11 Mar 18 Mar 25 Apr 01 Apr 08 Apr 15 2020 Figure 2. Number of estimated COVID-19 cases in Spain, inferred from the number of hospitalizations until April 15th 2020. The posterior mean of inferred cases is plotted in blue. Cumulative number of detected cases, hospitalizations and deaths are plotted in green, red and black curves, respectively. Grey curves represent the inferred number of cases in each autonomous community. The onset of state of emergency and mandatory confinement are indicated by a vertical bar. the expected numbers of events yi (r, d) in a certain autonomous We ran three alternative analyses: the principal analysis estimated communities is given by convolving the pattern of new cases with model parameters using hospitalizations reports; two control the distribution of infection-to-event: analyses were run using either detected cases or deaths reports,  which are two less reliable indicators. E [yi (r, d)] = pi N (c, t) li (d − t) (2) t