key: cord-0735306-q3xoodui authors: Garcia-Iglesias, Daniel; de Cos Juez, Francisco Javier title: Early behavior of Madrid Covid-19 disease outbreak: A mathematical model date: 2020-04-01 journal: nan DOI: 10.1101/2020.03.30.20047019 sha: 92eb8793c4b78ada457bff865a030947ef25ef5d doc_id: 735306 cord_uid: q3xoodui Introduction: Madrid Covid-19 disease outbreak started on 28 February 2020 and since then it became the main Covid-19 disease cluster in Spain. On 26 March 2020, a total of 17166 cases were already reported, with 2090 deaths. Globally a R0 index of 2-3 has been reported. We aimed to build an experimental mathematical model that help to analyze the early characteristics of Madrid Covid-19 disese outbreak and to explore the actual R0 index on Madrid Covid-19 outbreak. Material and Methods: A simulated mathematical model was built, based on a SIR epidemiological model and the reported characteristics of Wuhan Covid-19 disease outbreak. Monte Carlo simulations were further done to estimate the R0 value over time in the Madrid Covid-19 disease outbreak. Results: Mean estimated R0 value along the early period is of 2.22 (+/- 1.21 SD). A significant increase of 0.093 (+/- 0.037, p=0.025) in R0 value each day of outbreak is found. Conclussions: Our proposed Mathematical Simulation model may be useful to evaluate early characteristics of this outbreak. The present work is the first reported estimation of R0 value in the Spanish Madrid Covid-19 outbreak, with similar results to the previous reported in the Wuhan outbreak, although it may suggest a slightly increase on R0 along time. On 31 December 2019, a comunity-adquired pneumonia of unknown ethiology was first reported in Wuhan city. On 2 January 2020 it was first published its relation with a Coronaviridae virus, called SARS-CoV-2 (1) . During the first two months of epidemic, a total of 79384 cases were reported in China, with 2838 deaths (Lethal Index of 3.57% (2) . On 13 January 2020 the first case outside China was reported in Thailand, corresponding to an imported case from Wuhan and in the following days, imported cases from this region were also reported in Japan and Republic of Korea (3) . During the first 2 months of epidemia, a total of 85403 cases were globally reported, with a total of 2924 deaths and a Letality index of 3.42% (2) . In Spain, the first reported cases occurred on 31 January and 9 February 2020. They were two cases adquired on Germany and United Kingdom respectively(4 According to the early Wuhan outbreak data, the Reproduction Number (R 0 ) is reported to be between 2 and 3 [Li, Wu, Riou] . Although it may change over time and it can be reduced with PHM based on mobility restrictions, as it has been seen in Wuhan (8, 9) . To describe the early characteristics of Covid-19 outbreak in Madrid. To build a Mathematical model that fits the early findings of Covid-19 infection on Madrid's outbreak. Data used for this paper was obtained directly from Spanish Government reported cases. This data is available online at the Spanish Health Ministry webpage (10) . Analyzed data corresponds to the first 15 days of Madrid Covid-19 disease outbreak (26 February to 11 March 2020). Based on the Spanish Government reported cases, we built a stochastic transmission model, based on a classical SIR epidemiological model (11), as can be seen on figure 1 . Basically, it divides individuals into four different subgroups: Susceptible, Exposed, Infected and Removed (recovered, isolated or death). The incubation period was assumed to be Normally distributed, with a mean of 5 days and a standard deviation (SD) of 2 days. The time to the start of symptoms and the peak of the disease is normally distributed, with a mean of 3 days and a SD of 1 day. Once a patient is infected (turns into an Infected individual), the probability to transmit the infection on a certain day (R n ) is based on the estimated R 0 , with a peak probability on the peak day (p) of symptoms: The probability for developing symptoms is fixed on 0.7, and in those symptomatic patients, the time to diagnosis is Normally distributed, with a mean of 8 days and a SD of 2 days. Once a patient is diagnosed, it is supposed to be removed from the general population (turns into a Removed individual) and thus its probability to infect other individual is stopped. If a patient is asymptomatic and thus no diagnosed, it still can . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 infect other individuals up to 12 days (with a SD of 2 days) after the supposed peak of symptoms. All of this parameters introduced in the model are shown in table 1. The Mathematical model was built with R (12) and it can be downloaded online from our repository [cite] . Mean estimated R 0 value along the early period is of 2.22 (+/-1.21 SD). A temporal representation of the obtained R 0 value is shown in figure 2 , and temporal results with the confidence interval is also shown in table 2. During this analyzed period of time the regression analysis shows a significant increase of the R 0 value along days. An increase of 0.093 (+/-0.037, p=0.025) in R 0 value each day of outbreak is found. Simulated mathematical models are useful to asses the epidemic characteristics and evaluate possible effects of different PHM interventions. Moreover, they are of special interest in early stages of an outbreak, when no enough information is still available to make decisions. In this sense, the proposed model can be used and adapted to . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 evaluate the evolution of Covid-19 disease outbreak and to monitor the results of PHM undertaken by the governments. As described in the present work, the R 0 value in Madrid's Covid-19 disease outbreak (Spanish main Covid-19 disease outbreak) is similar to the reported in previous documents, corresponding to Wuhan outbreak (6,7). This R 0 value is about 2-3 at the beginning, although our data suggest it can increase along the outbreak if no PHM are taken. In previous reports, PHM based on mobility restrictions can reduce this R 0 value, leading to a disease control and finally to a possibility to overcome this situation. In this sense further investigation will be necessary to evaluate weather or not, this mobility restrictions can lead to a reduction in R 0 value. This effect in outbreak reduction would be of special importance to plan future decisions and to monitor their effect. Our proposed Mathematical Simulation model may be useful to evaluate early characteristics of this outbreak and the results of further PHM. The present work is the first reported estimation of R 0 value in the Spanish Madrid Covid-19 outbreak. It is similar to the previous reported in the Wuhan outbreak, although it may suggest a slightly increase on R 0 along time. Whether or not PHM based on mobility restrictions will be able to reduce R 0 value in Covid-19 Madrid outbreak is still not known, and thus, further investigation in this sense will be needed. . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 . CC-BY-NC 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 . https://doi.org /10.1101 /10. /2020 . CC-BY-NC 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 peer-reviewed) The copyright holder for this preprint . https://doi.org /10.1101 /10. /2020 Genomic characterization of the 2019 novel human-pathogenic coronavirus isolated from a patient with atypical pneumonia after visiting Wuhan World Health Organization. Novel Coronavirus(2019-nCoV) World Health Organization. Novel Coronavirus(2019-nCoV). Situation report 1 Actualización número 21. Neumonía por nuevo coronavirus COVID-19 Actualización número 36. Neumonía por nuevo coronavirus COVID-19 Coronavirus Disease 2019 in China Dynamic basic reproduction number based evaluation for current prevention and control of COVID-19 outbreak in China Estimation of the reproductive number of novel coronavirus (COVID-19) and the probable outbreak size on the Diamond Princess cruise ship: A data-driven analysis Enfermedad por nuevo coronavirus, COVID-19. Situación actual A contribution to the mathematical theory of epidemics R: A language and environment for statistical computing