Evaluación cuantitativa de un modelo SEIR para predecir casos de COVID-19 / Quantitative evaluation of a SEIR model for forecasting COVID-19 cases

Resumen Introducción : Los modelos epidemiológicos han sido ampliamente utilizados durante la pandemia de COVID-19, aunque la evaluación de su desempeño ha sido limitada. El objetivo del presente trabajo fue evaluar de forma retrospectiva un modelo SEIR para la predicción de casos a corto plazo (1 a 3 semanas), cuantificando su desempeño real y potencial, me diante la optimización de los parámetros del modelo. Métodos : Se realizaron proyecciones para cada día de la primera ola de casos (31 de julio de 2020 al 11 de marzo de 2021) en el municipio de General Pueyrredón (Argentina), cuantificando el desempeño del modelo en términos de incertidumbre, inexactitud e imprecisión. La evaluación se realizó con los parámetros originales del modelo (utilizados en proyecciones que fueron oportunamente publicadas), y luego variando distintos parámetros a fin de identificar valores óptimos. Resultados : El análisis del desempeño del modelo mostró que valores alternativos de algunos parámetros, y la corrección de los valores de entrada utilizando un filtro de "media móvil" para eliminar las variaciones semanales en los reportes de casos, habrían otorgado mejores resultados. El modelo con los parámetros opti mizados logró disminuir desde casi 40% a menos de 15% la incertidumbre, con valores similares de inexactitud, y con una imprecisión levemente mayor. Discusión : Modelos epidemiológicos sencillos, sin grandes requerimientos para su implementación, pue den ser de utilidad para la toma de decisiones rápi das en localidades pequeñas o con recursos limitados, siempre y cuando se tenga en cuenta la importancia de su evaluación y la consideración de sus alcances y limitaciones.

Abstract Introduction : Epidemiological models have been widely used during the COVID-19 pandemic, although performance evaluation has been limited. The objec tive of this work was to thoroughly evaluate a SEIR model used for the short-term (1 to 3 weeks) predic tion of cases, quantifying its actual past performance, and its potential performance by optimizing the model parameters. Methods : Daily case forecasts were obtained for the first wave of cases (July 31, 2020 to March 11, 2021) in the district of General Pueyrredón (Argentina), quantifying the model performance in terms of uncertainty, inac curacy and imprecision. The evaluation was carried out with the original parameters of the model (used in the forecasts that were published), and also varying different parameters in order to identify optimal values. Results : The analysis of the model performance showed that alternative values of some parameters, and the correction of the input values using a "mov ing average" filter to eliminate the weekly variations in the case reports, would have yielded better results. The model with the optimized parameters was able to reduce the uncertainty from almost 40% to less than 15%, with similar values of inaccuracy, and with slightly greater imprecision. Discussion : Simple epidemiological models, without large requirements for their implementation, can be very useful for making quick decisions in small cities or cities with limited resources, as long as the importance of their evaluation is taken into account and their scope and limitations are considered.

Evaluación de intervenciones durante la pandemia COVID-19: desarrollo de un modelo basado en subpoblaciones con distintas tasas de contacto / Evaluation of interventions during the COVID-19 pandemic: development of a modelbased on subpopulations with different contact rates

Resumen Si bien se han realizado múltiples intentos de modelar matemáticamente la pande-mia de la enfermedad por coronavirus 2019 (COVID-19), causada por SARS-CoV-2, pocos modeloshan sido pensados como herramientas interactivas accesibles para usuarios de distintos ámbitos.El objetivo de este trabajo fue desarrollar un modelo que tuviera en cuenta la heterogeneidadde las tasas de contacto de la población e implementarlo en una aplicación accesible, que per-mitiera estimar el impacto de posibles intervenciones a partir de información disponible. Sedesarrolló una versión ampliada del modelo susceptible-expuesto-infectado-resistente (SEIR),denominada SEIR-HL, que asume una población dividida en dos subpoblaciones, con tasas decontacto diferentes. Asimismo, se desarrolló una fórmula para calcular el número básico dereproducción (R0) para una población dividida en n subpoblaciones, discriminando las tasas decontacto de cada subpoblación según el tipo o contexto de contacto. Se compararon las pre-dicciones del SEIR-HL con las del SEIR y se demostró que la heterogeneidad en las tasas decontacto puede afectar drásticamente la dinámica de las simulaciones, aun partiendo de lasmismas condiciones iniciales y los mismos parámetros. Se empleó el SEIR-HL para mostrar elefecto sobre la evolución de la pandemia del desplazamiento de individuos desde posiciones dealto contacto hacia posiciones de bajo contacto. Finalmente, a modo de ejemplo, se aplicó elSEIR-HL al análisis de la pandemia de COVID-19 en Argentina; también se desarrolló un ejemplode uso de la fórmula del R0. Tanto el SEIR-HL como una calculadora del R0fueron implementadosinformáticamente y puestos a disposición de la comunidad.

Abstract Although multiple attempts have been made to mathematically model the currentepidemic of SARS-CoV-2, the causative agent of coronavirus disease 2019 (COVID-19), fewmodels have been conceived as accessible interactive tools for users from various backgrounds.The goal of this study was to develop a model that took into account the heterogeneity incontact rates within the population and to implement it in an accessible application allowingto estimate the impact of possible interventions based on available information. An extendedversion of the Susceptible-Exposed-Infected-Resistant (SEIR) model, named SEIR-HL, was deve-loped, assuming a population divided into two subpopulations, with different contact rates.Additionally, a formula for the calculation of the basic reproduction number (R0) for a popula-tion divided into n subpopulations was proposed, where the contact rates for each subpopulationcan be distinguished according to contact type or context. The predictions made by SEIR-HLwere compared to those of SEIR, showing that the heterogeneity in contact rates can drama-tically affect the dynamics of simulations, even when run from the same initial conditions andwith the same parameters. SEIR-HL was used to predict the effect on the epidemic evolution ofthe displacement of individuals from high-contact positions to low-contact positions. Lastly, byway of example, SEIR-HL was applied to the analysis of the SARS-CoV-2 epidemic in Argentinaand an example of the application of the R0formula was also developed. Both the SEIR-HLmodel and an R0calculator were computerized and made available to the community.

Research progress of infectious disease dynamics models / 预防医学

@#The management of emerging infectious diseases has always been given a high priority in public health. Identification of the epidemiological characteristics and transmission patterns of emerging infectious diseases is of great significance to contain the disease transmission and reduce the damages to public health and socioeconomic developments. Currently, infectious disease dynamics models are mainly established based on infectious disease surveillance data to predict the epidemiological patterns and trends of emerging infectious diseases; however, many model-based predictions fail to achieve the expected results due to the presence of multiple uncertain factors during the integrated management of infectious diseases. This review describes the basic principles and variables of common infectious disease dynamics models, including the susceptible-infected-recovered ( SIR ) model, susceptible-infected-removed-susceptible ( SIRS ) model, susceptible-exposed-infected-removed ( SEIR ) model and improved SEIR model, compares the advantages and disadvantages of these models, and summarizes the advances of the infectious disease dynamics models in the prediction of trends in incidence of emerging infectious diseases, so as to provide insights into the effective application of infectious disease dynamics models in the management of infectious diseases.

ANOVA to Compare Three Methods to Track COVID-19 in Nine Countries / ANOVA en la comparación de tres métodos para rastrear COVID-19 en nueve países

ABSTRACT A new coronavirus denominated first 2019-nCoV and later SARS-CoV-2 was found in Wuhan, China in December of 2019. This paper compares three mathematical methods: nonlinear regression, SIR, and SEIR epidemic models, to track the covid-19 disease in nine countries affected by the SARS-CoV-2 virus, to help epidemiologists to know the disease trajectory, considering initial data in the pandemic, mainly 100 days from the beginning. To evaluate the results obtained with the three methods one-way ANOVA is applied. The average of predicted infected cases with SARS-CoV-2, obtained with the mentioned methods was: for United States of America 1,098,508, followed by Spain with 226,721, Italy with 202,953, France with 183,897 United Kingdom with 182,190, Germany with 159,407, Canada with 58,696, Mexico with 50,366 and Argentina with 4,860 in average. The one-way ANOVA does not show a significant difference among the results of the projected infected cases by SARS-CoV-2, using nonlinear regression, SIR, and SEIR epidemic methods. The above could mean that initially any method can be used to model the pandemic course.

RESUMEN Un nuevo coronavirus denominado primero 2019-nCoV y más tarde SARS-CoV-2 fue encontrado en Wuhan, China en diciembre de 2019. El objetivo de este trabajo es comparar tres métodos matemáticos: regresión no lineal, modelos epidemiológicos SIR y SEIR, para rastrear la enfermedad del COVID-19 en nueve países infectados por el virus SARS-CoV-2, con el propósito de ayudar al epidemiólogo a conocer el curso de la pandemia, considerando principalmente sus primeros 100 días. Para evaluar los resultados obtenidos de la aplicación de los tres métodos, se aplicó ANOVA de una vía. El número promedio de casos infectados con SARS-CoV-2, obtenidos con los tres métodos descritos son: para Estados Unidos 1,098,508, seguido de España con 226,721, Italia con 202,953, Francia con 183,897 Reino Unido con 182,190, Alemania con 159,407, Canadá con 58,696, México con 50,366 y Argentina con 4,860 en promedio. El ANOVA de una vía no muestra diferencias significativas entre los resultados de los casos infectados proyectados por SARS-CoV-2, utilizando la regresión no lineal y los métodos SIR and SEIR. Lo anterior podría señalar que cualquiera de los tres métodos estudiados puede modelar el curso de la pandemia en las condiciones descritas para cada uno.

Modeling transmission dynamics of severe acute respiratory syndrome coronavirus 2 in São Paulo, Brazil

Abstract INTRODUCTION Severe acute respiratory syndrome coronavirus 2 has been transmitted to more than 200 countries, with 92.5 million cases and 1,981,678 deaths. METHODS This study applied a mathematical model to estimate the increase in the number of cases in São Paulo state, Brazil during four epidemic periods and the subsequent 300 days. We used different types of dynamic transmission models to measure the effects of social distancing interventions, based on local contact patterns. Specifically, we used a model that incorporated multiple transmission pathways and an environmental class that represented the pathogen concentration in the environmental reservoir and also considered the time that an individual may sustain a latent infection before becoming actively infectious. Thus, this model allowed us to show how the individual quarantine and active monitoring of contacts can influence the model parameters and change the rate of exposure of susceptible individuals to those who are infected. RESULTS The estimated basic reproductive number, R o , was 3.59 (95% confidence interval [CI]: 3.48 - 3.72). The mathematical model data prediction coincided with the real data mainly when the social distancing measures were respected. However, a lack of social distancing measures caused a significant increase in the number of infected individuals. Thus, if social distancing measures are not respected, we estimated a difference of at least 100,000 cases over the next 300 days. CONCLUSIONS: Although the predictive capacity of this model was limited by the accuracy of the available data, our results showed that social distancing is currently the best non-pharmacological measure.

Modeling of a coronavirus disease outbreak at the beginning of 2021 in Shijiazhuang， Hebei Province， China / 上海预防医学

Objective:To model an outbreak of coronavirus disease 2019 （COVID-19） in Shijiazhuang and forecast its spread trend. Method:We collected confirmed COVID-19 cases from the Health Commission of Hebei Province during the period of January 2 to January 27， 2021. We built a new model （SEIaIcRK）， including the contribution of asymptomatic cases， based on the traditional SEIR model to explore and analyze the transmission of COVID-19. Results:A total of 863 confirmed cases were reported during the study period （ended on January 27， 2021）. Our model fitted well with the daily cumulative incidence data and showed that the effective reproductive number decreased sharply from 3.80 on January 2 to 1.54 on January 4， then further decreased to <1 afterwards. Our model also predicted that number of COVID-19 cases would not increase after Feb 16， 2021. Conclusion:The SEIaIcRK model can be used to predict the spread trend of COVID-19 in Shijiazhuang. The current COVID-19 countermeasures effectively contain the disease spread.

Assessment and prediction of the oversea imported risk of COVID-19 in Shanghai / 上海预防医学

Objective To determine the association between global epidemic of COVID-19 and local situation of imported cases from abroad to Shanghai, and then to predict the risk of imported COVID-19 epidemic from December 2020 through March 2021. Methods A retrospective analysis on the imported COVID-19 cases from abroad to Shanghai was conducted. The correlation between global and country-specific confirmed COVID-19 cases(weekly confirmed cases per 100 000 population)and imported cases(weekly reported)in Shanghai was determined. Compared to the risk in November 2020, country-specific risk of imported cases to Shanghai was assessed to calculate the possible number of imported case in the near future using SEIR model. Results The number of imported case of COVID-19 from abroad to Shanghai increased along with the global epidemic, with several peaks accordingly. However, the imported cases did not accumulate, as potential epidemic has been always effectively contained through timely implementation of prevention and control measures. The number of weekly imported cases in Shanghai was significantly correlated with the number of global weekly confirmed cases per 100 000 population(rSpearman = 0.349, P = 0.029), and also correlated with weekly reported cases in certain countries(P < 0.05), such as the UK and France. Using the number of imported cases from abroad to Shanghai in November as baseline, the estimated monthly number of imported cases in Shanghai might increase in the following four months. Conclusion The risk of imported COVID-19 cases from abroad to Shanghai may increase in the near future. Prediction of imported case would provide scientific evidence for optimizing prevention and control measures and reserving medical resources for the imported epidemic.

Spatial accessibility of fever clinics for multi-tiered prevention and control on COVID-19 in Beijing / 北京大学学报(医学版)

OBJECTIVE@#To simulate the different prevalence of corona virus disease 2019 (COVID-19) in Beijing as the spreading and the outbreak city and analyze the response capacity of its medical resources of fever clinics, and to provide a scientific basis for optimizing the spatial layout in Beijing under severe epidemics.@*METHODS@#The study obtained epidemiological indicators for COVID-19, factors about medical resources and population movement as parameters for the SEIR model and utilized the model to predict the maximum number of infections on a single day at different control levels in Beijing, simulated as an epidemic spreading city and an epidemic outbreak city respectively. The modified two-step floating catchment area method under ArcGIS 10.6 environment was used to analyze spatial accessibility to fever clinics services for the patients in Beijing.@*RESULTS@#According to the results of the SEIR model, the highest number of infections in a single day in Beijing simulated as an epidemic spreading city at low, medium and high levels of prevention and control were 8 514, 183, and 68 cases, the highest number of infections in a single day in Beijing simulated as an outbreak city was 22 803, 10 868 and 3 725 cases, respectively. The following result showed that Beijing was simulated as an epidemic spreading city: among the 585 communities in Beijing, under the low level of prevention and control, there were 17 communities (2.91%) with excellent accessibility to fever clinics, and that of 41 communities (7.01%) with fever clinics was good. Spatial accessibility of fever clinics in 56 communities (9.57%) was ranked average, and 62 communities' (10.60%) accessibility was fair and 409 communities (69.91%) had poor accessibility; at the medium level of prevention and control, only the west region of Fangshan District and Mentougou District, the north region of Yanqing District, Huairou District and Miyun District had poor accessibility; under the high level of prevention and control, 559 communities' (95.56%) had excellent accessibility. The accessibility in 24 communities (4.10%) was good and in 2 communities (0.34%) was average. In brief, the existing fever clinics could meet the common demand. Beijing was simulated as an outbreak city: under the low level of prevention and control, only 1 community (0.17%) had excellent accessibility to fever clinics, and 5 communities (0.86%) had good accessibility. The accessibility of fever clinics in 10 communities (1.71%) was average and in 12 communities (2.05%) was fair. The accessibility of fever clinics in 557 communities (95.21%), nearly all areas of Beijing, was poor; under the middle and high level of prevention and control, the accessibility of ecological conservation areas was also relatively poor.@*CONCLUSION@#The distribution of fever clinic resources in Beijing is uneven. When Beijing is simulated as an epidemic spreading city: under the high level of prevention and control, the number of fever clinics can be appropriately reduced to avoid cross-infection; at the medium level of prevention and control, the fever clinics can basically meet the needs of patients with fever in Beijing, but the accessibility of fever clinics in ecological conservation areas is insufficient, and priority should be given to the construction of fever clinics in public hospitals above the second level in the ecological conservation areas. When the level of prevention and control is low, the accessibility of fever clinics in ecological conservation areas is poor. Priority should be given to the construction of fever clinics in ecological conservation areas, and temporary fever sentinels can be established to relieve the pressure of fever clinics. When Beijing is simulated as an outbreak city and has low prevention and control, due to a large number of infections, it is necessary to upgrade the prevention and control level to reduce the flow of people to curb the development of the epidemic.

Retrospective analysis of Chinese epidemic situation model based on elbow cluster analysis / 上海交通大学学报（医学版）

Objective • To explore the correlation patterns of the new coronavirus disease 2019 (COVID-19) epidemic in various provincial administrative regions in China at the early stage of the epidemic, and forecast the following development of epidemic situation. Methods • The data on the COVID-19 epidemic situation in various provincial administrative regions in China published by National Health Commission of People's Republic of China from Jan. 13 to Feb. 13, 2020, were retrospectively analyzed. The elbow cluster analysis method was used to cluster the provincial administrative regions. The SEIR (susceptible-exposed-infectious-recovered) model was used to calculate the basic infection number (R0) of different clusters, whose changing trends were also predicted. Results • According to the prevalence rates, the 34 provincial administrative regions were divided into four types of clusters: Cluster (22 provincial administrative regions), Cluster Ⅱ (9 provincial administrative regions), Cluster III (2 provincial administrative regions) and Cluster (Hubei). The prevalence rate of Hubei was higher than those of other clusters (P=0.000), but the differences in the cure rate and the case-fatality rate among the four clusters were not statistically significant; the R0 values based on the SEIR model of them were 2.764, 3.056, 3.899 and 3.984, respectively. By Feb. 13, 2020, except for Hubei, the cumulative prevalence curves of the other clusters tended to be stable and the cure rates increased. The prevalence rate and case-fatality rate of Hubei were still higher, and the cure rate was lower. Conclusion • From Jan. 13 to Feb. 13, 2020, 34 provincial administrative regions in China can be divided into four clusters according to the severity of the COVID-19 epidemic, and the prevalence rate of Cluster was significantly higher than those of other three clusters; by Feb. 13, 2020, the epidemic situations in the Cluster , Ⅱ and III has been alleviated, and the epidemic situation in Cluster areas were still severe.

Fitting and forecasting the trend of COVID-19 by SEIR+ CAQ dynamic model / 中华流行病学杂志

Objectives@#Fitting and forecasting the trend of COVID-19 epidemics.@*Methods@#Based on SEIR dynamic model, considering the COVID-19 transmission mechanism, infection spectrum and prevention and control procedures, we developed SEIR+ CAQ dynamic model to fit the frequencies of laboratory confirmed cases obtained from the government official websites. The data from January 20, 2020 to February 7, 2020 were used to fit the model, while the left data between February 8-12 were used to evaluate the quality of forecasting.@*Results@#According to the cumulative number of confirmed cases between January 29 to February 7, the fitting bias of SEIR+ CAQ model for overall China (except for cases of Hubei province), Hubei province (except for cases of Wuhan city) and Wuhan city was less than 5%. For the data of subsequent 5 days between February 8 to 12, which were not included in the model fitting, the prediction biases were less than 10%. Regardless of the cases diagnosed by clinical examines, the numbers of daily emerging cases of China (Hubei province not included), Hubei Province (Wuhan city not included) and Wuhan city reached the peak in the early February. Under the current strength of prevention and control, the total number of laboratory- confirmed cases in overall China will reach 80 417 till February 29, 2020, respectively.@*Conclusions@#The proposed SEIR+ CAQ dynamic model fits and forecasts the trend of novel coronavirus pneumonia well and provides evidence for decision making.

Application of epidemic dynamics model in isolating hospital-acquired rotavirus infection / 中国感染控制杂志

Objective To establish an epidemic dynamics model of the transmission and prevention strategies of rotavirus infection in hospital.Methods Rotavirus SEIR model based on different isolation measures was constructed using epidemic dynamics method, the effectiveness of isolation measures was evaluated.Results Supposing that all patients were isolated, isolation measures were taken on the 3rd day of transmission, there were 4.3 cases of infection on the 5th day of transmission, peaked on the 7th day(n=6.4), until the 14th day of transmission, the number of infected persons fell to 3.4 cases.If isolation measures were taken on the 2nd day of transmission, the infected persons reached 4.0 on the 6th day, and reduced to 3.2 cases on the 8th day.If isolation measures were taken on the 1st day of transmission, the infected persons reached 2.4 at most, healthcare-associated infection would not occur.Early isolation can effectively prevent the outbreak of rotavirus infection, the later the isolation, the more the infection occurs and the longer the outbreak lasts.Conclusion Rotavirus infection can easily break out in hospital, early discovery and early isolation of rotavirus infected child is the effective measure to avoid rotavirus infection outbreak in hospital.