key: cord-0994179-66gvfopd authors: Bae, Tae Wuk; Kwon, Kee Koo; Kim, Kyu Hyung title: Mass Infection Analysis of COVID-19 Using the SEIRD Model in Daegu-Gyeongbuk of Korea from April to May, 2020 date: 2020-08-26 journal: J Korean Med Sci DOI: 10.3346/jkms.2020.35.e317 sha: 4667156b5fcf9161b2a280be83b269bb4b1996cb doc_id: 994179 cord_uid: 66gvfopd BACKGROUND: The novel coronavirus (coronavirus disease 2019 [COVID-19]) outbreak began in China in December last year, and confirmed cases began occurring in Korea in mid-February 2020. Since the end of February, the rate of infection has increased greatly due to mass (herd) infection within religious groups and nursing homes in the Daegu and Gyeongbuk regions. This mass infection has increased the number of infected people more rapidly than was initially expected; the epidemic model based on existing studies had predicted a much lower infection rate and faster recovery. METHODS: The present study evaluated rapid infection spread by mass infection in Korea and the high mortality rate for the elderly and those with underlying diseases through the Susceptible-Exposed-Infected-Recovered-Dead (SEIRD) model. RESULTS: The present study demonstrated early infection peak occurrence (-6.3 days for Daegu and -5.3 days for Gyeongbuk) and slow recovery trend (= -1,486.6 persons for Daegu and -223.7 persons for Gyeongbuk) between the actual and the epidemic model for a mass infection region compared to a normal infection region. CONCLUSION: The analysis of the time difference between infection and recovery can help predict the epidemic peak due to mass (or normal) infection and can also be used as a time index to prepare medical resources. The novel coronavirus (coronavirus disease 2019 ) outbreak began in Wuhan, China in December 2019 and has spread to at least 177 countries. 1 According to the World Health Organization (WHO) report, 2 as of 5 August 2020, COVID-19 has killed more than 696,147 people so far, with more than 18.3 million confirmed cases globally. Symptoms of COVID-19 are not specific and the disease manifestation can vary from no symptoms (asymptomatic) to severe pneumonia and death. According to a WHO report based on 55,924 laboratory-confirmed cases, 3 typical signs and symptoms include fever, dry cough, fatigue, sputum production, shortness of breath, and sore throat. In the case Researchers at UT-Austin in the US analyzed about 450 cases of infection in 93 cities in China and found that more than 10% of the confirmed cases were asymptomatic. 8 The period of serial interval (continuous infection) of the virus, which was the time taken from the time the infected person showed symptoms until the second infected person showed symptoms, was only 4 days on average. As a measure of the transmission rate of infectious diseases, the shorter the serial interval, the faster the transmission rate. In the study, the rate of transmission of COVID-19 was analyzed to be as fast as the seasonal flu. In order to respond to the rapid spread of COVID-19, appropriate virus spread models should be established for each country, and accordingly, inspection kits, screening clinics, and infectious disease treatment hospitals should be equipped more rapidly and aggressively. Unlike the general spread of viruses, the new coronavirus spread rapidly in Korea, mainly from religious groups and nursing homes. 9 Through these collective infections, the new virus spread rapidly within a much shorter time than the infectious disease spreading curve of the infectious disease spread model. In particular, most of the elderly patients in nursing homes have significant underlying diseases, and due to additional COVID-19 infection, the mortality rate in Korea was higher compared to the mortality rate for common COVID-19 infection. In this paper, we analyzed the rapid virus spread and recovery trend by mass infection in Korea using the Susceptible-Exposed-Infected-Recovered-Dead (SEIRD) model. 10 By analyzing the inconsistency between the SEIRD model and the trend of infection caused by mass infections, this study derives the infection reproduction number, the date of the inflection point, the mortality rate of the elderly with underlying disease, and the difference between the epidemic peak and recovery for each region. This section describes the basic SEIRD model, 10,11 important parameter settings in published epidemic models, 12-32 and the infection-reproduction equation. The individuals of the SEIRD model are classified into four types, S(t), E(t), I(t), R(t) and D(t) which denote the number of people susceptible, exposed, infected, and recovered on day t (Supplementary Fig. 1 ). The SEIRD model is defined by a system of 5 ordinary differential equations as follows: (1) where β, δ, and γ denote the transmission rate, the infection (onset) rate, and the recovery rate, respectively. β(= R 0 γ) is obtained by R 0 , the initial infection-reproduction number. δ(= 1/c) and γ(= 1/h) are calculated by c, the incubation (latent) period, and h, the hospitalization (infectious) period, respectively. ρ(= 1/d) is the rate at which people die and d is the infectiondeath period (i.e. days from infection to death). α is the death fatality rate. The estimated values of important parameters of COVID-19 was analyzed in recently studied epidemic models (Supplementary Table 1 ). The parameters for the SEIRD model were set by the data analysis results for Wuhan city, China and Gyeongbuk, Daegu, Korea. We assumed no further transmission would occur once a person entered into the status of R. S was set to (P-I[0]-E[0]), total city population (P) excluding the initially infected and exposed population. 9 E was set as 20 times that of I in accordance with Wang et al. 12 and Read et al. 13 R(0) and D(0) were set as 0. The mean incubation period of the new coronavirus was determined to be 5.2 days according to previously published studies. 14-17 Therefore, δ was set as 0.1923(= 1/5.2) with reference to previously published studies. 14-16,18,20 In some 12, 22 though not all 21 previous studies, the average hospitalization period including the mean time from pathogenesis (disease onset) to diagnosis was calculated as 18 days. The median time from disease onset to diagnosis among confirmed patients was previously found to be 5 days. 23 On this basis, our γ was set as 0. The infection-reproduction number, R 0 , represents the average number of new infections spread by each infected person. The average number of secondary infections (reproduction function) at time t is expressed as R 0 (t). R 0 should be carefully selected because it greatly affects the spread curve of the spread model. 15,21,28, 29 The number of secondary infections at time t is given as follows: where R 0S (= 3.7 and 2.7 for Daegu and Gyeongbuk respectively) and R 0E (= 0.5 for both regions) are the reproduction number at the beginning and end of the spread of infectious diseases. The t d (= 12 and 9 days for Daegu and Gyeongbuk respectively) represent the date of the inflection point and the steepest decline of R 0 . It could be thought of as the main lockdown date and was set based on the date that infection rates began to decrease after the explosion of infection rates in Daegu and Gyeongbuk. The k(= 0.5) indicates the declination rate of R 0 . In addition, the declination rate was set in consideration of the rapid increase and decrease of infection. In a previous study, β was used as an inferred value via a least-square-based procedure with Poisson noise 15 and Markov Chain Monte Carlo 29 or preset constants. 30 In this paper, β(= R 0 γ) is obtained by R 0 and γ. Results from the SEIRD model for the Daegu-Gyeongbuk region are shown in Fig. 1 . The graph was modeled based on actual data from the start of infection and for an 84-day period. The figure shows the distribution of I (infections) and D (deaths) for the left Y-axis and R (recovered) for the right Y-axis. From the actual data for Daegu and Gyeongbuk, the number of infected persons exploded after the 10th day from the start of the spread of the infectious disease. This is due to the collective infections that occurred through Sinchonji religious groups and nursing homes. To quantitatively confirm the actual infection curve, 6th order polynomial curve fitting was also applied. It is not easy to estimate the rapid increase in the number of infected people due to the (incidental) collective infection as an existing SEIRD model. In the case of mass infections, such as in religious groups or nursing homes in Korea, epidemic peaks may occur earlier compared to predictions made by common SEIRD models. In other words, collective infection means that the time to prepare health care resources before the spread of infectious diseases can be much shorter than we thought. Although the t d was set considering the period of the mass infection described in Fig. 1A order to find differences in the actual and estimated trends for those recovering from COVID, the date d R.C occurs when the actual and estimated numbers of those recovering are equal and the number of those recovering h R.C at that time is defined. The averages, � C.a and � C.m , of the actual and modeled recovery numbers are compared. It was found that mass infection by COVID-19 may cause a difference hd R.C ( � C.a − � C.m ) in the number of those recovering after The delay of actual recovery can be confirmed in a recent report on the release of containment in Daegu city. 9 In the simulation of this paper, the hospitalization period was set to 18 days based on the results of existing COVID-19 studies, 12,22 but the actual recovery trend was not accurately predicted. The results of these recovery simulations indicate that recovery delays may occur by country and region. According to Daegu city, 9 as a result of investigating the treatment period of about 5,000 diagnosed patients, the average treatment period was 24.8 days. It was found that it took more than 20 days for 73% of all confirmed cases in Daegu to be cured. In addition, the average treatment period for people who healed completely from COVID-19 and were under the age of 30 was 24.7 days, and the treatment period between the ages of 30 and 69 years was 24.8 days; thus there was little difference in treatment period by age group observed in our study. We further note that the treatment period for patients aged 70 or older was 25.6 days, similar to other treatment periods. As shown in Table 2 , the average duration of release of sequestered patients by management type was 25.3 days for hospitals, 24.4 days for living treatment facilities, and 22.7 days for self-isolation. In addition, it took a little longer for the relatively severe patients admitted to the hospital to be released from quarantine. Daegu (R 0S = 3.7) has a much higher reproduction number than other regions due to group infections among the Shincheonji religious group, while Gyeongbuk (R 0S = 2.6) has the next highest reproduction number due to group infections in nursing hospitals where senior citizens are hospitalized. The number of infected people in Gyeongbuk increased rapidly from the date of infection, similar to Daegu, but the reproduction number was smaller than that of Daegu. Table 2 , resulting in a delay in the actual recovery trend. While Gyeonggi had a high mortality rate compared to the number of confirmed patients, Seoul's mortality rate was significantly lower than in other regions. In Seoul and Gyeonggi, the reproduction number is small due to the small number of general infections, and the t d is high (gentle descent) due to a long-term irregular small-scale spread. Using the reproduction equation (equation 6), it was found that the reproduction number and t d are inversely related (R 0S ∝ 1/t d ) regardless of the mass infection and the general infection. This implies that when sufficient COVID-19 infection data is available, the t d corresponding to the reproduction number can be deduced. In this section, we comprehensively analyzed the difference of epidemic peaks and the number of those recovering in the actual trend and the epidemic model for cities in Korea. Table 3 shows the result of parameters related to infections and recoveries for the actual and modeled trend of COVID-19 in the cities of Korea. It is necessary to note that the actual (as well as modeled) epidemic peaks and the cross date (d R.C ) of the actual and modeled recovery curves were different in Daegu-Gyeongbuk, where small mass infection occurred, and The parameters used in this paper were analyzed based on the resulting trends. If only the initial infection trend is given without prior information of the mass infection, the actual epidemic peak may appear much faster than the epidemic peak predicted by the model. The infection trend predicted in the SEIRD model 10,11 was greatly influenced by the transmission rate and incubation period, and these two variables were dominant factors in the actual infection trend. As a result, actual and predicted infection trends had morphological similarities. Therefore, it is easy to compare actual and predicted infection trends based on infection peaks. On the other hand, recovery trend prediction was affected by the recovery rate and fatality rate, but it was not easy to apply the values of these variables to any region or country to predict. Actually, for COVID-19, the recovery rates investigated in several studies 12,14-16,18,21,24 had the largest minimum-to-maximum ratio compared to other variables. In addition, the recovery trend, unlike the infection trend, had no characteristic points that can be used as a reference point. For this reason, in the comparison of recovery trends, the difference in the number of recoverers was used, not the time (day). In the recovery trend, the crossing date and the number of those recovering at that time were used to analyze whether the model follows the actual recovery trend. The fast crossing time meant that the model deviated faster from the actual recovery trend. The crossing dates of Daegu-Gyeongbuk and Seoul-Gyeonggi were d R.C = 50, 45 and d R.C = 75, 74, respectively. The recovery crossing dates in the Daegu-Gyeongbuk (mass infection) were earlier than in the Seoul-Gyeonggi (normal infection). This was because the actual recovery in the Daegu-Gyeongbuk region was slower than what was predicted by the epidemic model due to the long hospitalization period, while the used epidemic model for Seoul-Gyeonggi followed the actual recovery trend. In conclusion, the faster crossing time in Daegu-Gyeongbuk could lead to a large discrepancy between the actual number of those recovering and the number of recovering COVID-19 patients predicted by the model, as described in the mass infection analysis. overcrowded regional hospital resources and forced some confirmed patients to stay at home. Fig. 3 shows the trend of daily (infections and deaths) and cumulative (total infections and total recovered) COVID-19 confirmed patients in Daegu, Gyeongbuk, Seoul, and Gyeonggi. 9 Since national patient number 31, belonging to a religious group, was reported on higher than the rates in previous reports. 25,26 This value was higher than the mortality rate for participants in their 60s (60-69), which was also due to the mass infection of the elderly with underlying diseases in nursing homes, the main infectious factor in the Gyeongbuk. In addition, the relatively high mortality rate in Daegu was due to mass infections among religious groups, and it was estimated that the age range of infected people in Daegu was rather high. Mortality rates from previous studies did not adequately estimate the death curve for the elderly with mass infection and underlying disease, because most of the deaths in Korea were those with underlying disease who were over 60 years of age. Because the number of infected people in Seoul and Gyeonggi was much lower than that of Daegu and Gyeongbuk, it was not easy to infer the correlation between mortality rate due to normal infection and age and underlying disease in their region. Unlike the general virus outbreak, the spread of COVID-19 in Korea has been rapid, particularly in closed spaces such as religious organizations and nursing homes in Daegu-Gyeongbuk. In contrast, general community infections excluding such closed spaces progressed slowly due to the active use of masks and disinfectants by citizens. Therefore, the rapid spread in the early stages of infection was limited to specific religious groups and nursing hospital communities rather than representing all of Daegu-Gyeongbuk (or Korea). It may be difficult to estimate the spread of the virus due to such an unusual mass infection using a general epidemic model. The spread and status of COVID-19 in Daegu-Gyeongbuk was as follows. First, the number of infected people in Daegu-Gyeongbuk accounted for 76% of the total number of infected people in Korea, and it had spread to specific communities within Daegu-Gyeongbuk. Second, the explosion of infection occurred within 10 days after the initial infection and lasted for 2 weeks, and then began to fade. Third, due to active social distance and the use of masks, the proliferation of communities with COVID-19 outbreaks other than specific communities that were sources of infection had progressed relatively slowly. Fourth, largescale examinations through screening clinics and drive-through examinations in the early stages of the spread of infection enabled accurate statistics of the increase in confirmatory patients. Fifth, Korea has a high patient acceptance rate of treatment facilities that can cope with the rapidly growing confirmed infection rates. characteristics of the epidemic itself, such as asymptomatic infection, the population density of the affected area, and social distancing. In this paper, the characteristics of mass infection and asymptomatic infection were inferred by analyzing the difference between the actual and predicted infection peaks as well as the accuracy of the used epidemic model. Table 5 shows the time taken from first infected person to peak infection in various countries. The time taken to peak infection in Daegu and Gyeongbuk was achieved in a very short time compared to other countries. It may be due to mass infections through religious groups and nursing hospitals and asymptomatic infection of COVID-19. And this rapid infection peak also occurred in China and Italy. In China, the actual peak date of infection in the public data 34 and the trend of 3-day average of new confired cases 37 was much faster than the estimated peak date in the phaseadjusted estimation method. 12 And in the case of Italy as well, the actual infection peak time in the trend of 3-day average of new confired cases 37 was much faster than the predicted infection peak time in the improved epidemic dynamics model. 35 This early infection peak is likely related to asymptomatic infection of COVID-19. 35 used a modified SEIR model including an asymptomatic infection variable to predict the epidemic peak in Italy. As a result, the method shows a relatively small peak date difference between the actual and predicted peaks despite the large infection scale in Italy. As a result, this paper infers that in Daegu-Gyeongbuk, the high population density of religious organizations and nursing hospitals and the amplification of infections caused by asymptomatic infection of COVID-19 (long incubation period) significantly advanced the epidemic peak date compared to other countries or cities. It is not easy to explain the mass infections in Daegu-Gyeongbuk described above as a general epidemic model. Although the parameters used in the SEIRD model were set based on the results of a recent COVID-19 study, the model used did not accurately describe the spreading characteristics within Daegu-Gyeongbuk. Nevertheless, this paper analyzed the early appearance of epidemic peaks and slow recovery trends by mass infection by comparing the difference between epidemic peaks and recovery trends between the actual trend and the epidemic model. This characterization of mass infection is useful for inferring the preparation time of necessary medical resources in the future, and can also be used to derive the hospitalization period of the infectious group (older in this paper than in previous research) that directly affects the recovery trend. Mass infection was the largest factor affecting the COVID-19 spread in Korea and occurred intensively in a short period of time, earlier than the epidemic peak date predicted in the existing SEIRD model. Modeling studies of mass infections have more variables to be considered compared to general virus outbreaks. When a mass infection occurs, the initial virus response time is much shorter than for normal spread. Therefore, in order to prepare for the second epidemic of COVID-19, rapid research on collective infections by country and region is essential, and a command system should be established to prepare medical resources within the predicted epidemic peak date. COVID-19: a novel zoonotic disease caused by a coronavirus from China: what we know and what we don World Health Organization. Coronavirus disease (COVID-19) pandemic Report of the WHO-China joint mission on coronavirus disease COVID-19: consider cytokine storm syndromes and immunosuppression Recurrence of positive SARS-CoV-2 RNA in COVID-19: a case report Are coronavirus tests accurate? Diagnosis of the coronavirus disease (COVID-19): rRT-PCR or CT? Serial interval of COVID-19 among publicly reported confirmed cases Trend of reported cases The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda Monitoring Italian COVID-19 spread by an adaptive SEIRD model Phase-adjusted estimation of the number of coronavirus disease 2019 cases in Wuhan Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions Transmission dynamics of 2019 novel coronavirus (2019-nCoV) Mass Infection Analysis in Daegu-Gyeongbuk of Korea 15. Kuniya T. Prediction of the epidemic peak of coronavirus disease in Japan, 2020 Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study Preliminary prediction of the basic reproduction number of the Wuhan novel coronavirus 2019-nCoV Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data Reactive Social distancing in a SIR model of epidemics such as COVID-19 Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China Tracking and predicting COVID-19 epidemic in China mainland Analysis on 54 mortality cases of coronavirus disease 2019 in the Republic of Korea from Report on the epidemiological features of coronavirus disease 2019 (COVID-19) outbreak in the Republic of Korea from Domestic occurrence status Early dynamics of transmission and control of COVID-19: a mathematical modelling study Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions A simulation on potential secondary spread of novel coronavirus in an exported country using a stochastic epidemic SEIR model Risk assessment of novel coronavirus COVID-19 outbreaks outside China COVID-19 pandemic in Hubei Improved epidemic dynamics model and its prediction for COVID-19 in Italy COVID-19 pandemic in Greece An examination on the transmission of COVID-19 and the effect of response strategies: a comparative analysis Supplementary Fig. 1 Transition configuration of Susceptible-Exposed-Infected-Recovered-Dead model.