Epidemias en la actualidad: de cómo los modelos matemáticos y estadísticos permiten entenderlas, aún a profesionales "adversos" a ellos / Mathematical models to understand pandemics

Since the declaration of SARS CoV-2 pandemic, we have witnessed an accelerated increase in new cases, frequently associated with the need for intensive care and mechanical ventilation. In parallel, we have been invaded by many experts in the press and who expose their knowledge on the behavior of epidemics who use concepts that are not always well understood by the medical community. Some concepts should be knowledgeable to understand the epidemic spread. First, the epidemic spread description is not modeled with an exponential curve, but rather with a Gompertz curve. Second, a gamma curve describes the period of contagiousness. Third, the contagion magnitude or rate can be calculated and modeled. Explaining these mathematical concepts in a simple and graphic way will allow readers to understand better what is happening with the current pandemic.

Predictive model for Covid-19 incidence in a medium-sized municipality in Brazil (Ponta Grossa, Paraná) / Modelo predictivo de la ocurrencia de Covid-19 en un municipio de tamaño medio en Brasil (Ponta Grossa-Paraná) / Modelo preditivo da ocorrência de Covid-19 em município de médio porte no Brasil (Ponta Grossa-Paraná)

ABSTRACT Objective: to produce a predictive model for the incidence of COVID-19 cases, severity and deaths in Ponta Grossa, state of Paraná. Methods: this is an ecological study with data from confirmed cases of COVID-19 reported between March 21, 2020 and May 3, 2020 in Ponta Grossa and proportion of severity, hospitalization and lethality in the literature. A susceptible-infected-recovered (SIR) epidemic model was developed, and reproduction rate (R0), duration of epidemic, peak period, number of cases, hospitalized patients and deaths were estimated. Deaths were calculated by age group and in three scenarios: at day 24, at day 34, and at day 44 of the epidemic. Results: in the three scenarios assessed in this study, the variation in the number of cases was explained by an exponential curve (r2=0.74, 0.79 and 0.89, respectively, p<0.0001 in all scenarios). The SIR model estimated that, in the best scenario, the peak period will be around 120 days after the first case (between July 11, 2020 and July 25, 2020), estimated R0 will be 1.07 and will infect 0.23% of the population. In the worst scenario, peak period will involve 4,375 (95% CI; 4156-4594) cases and 825 (95% CI; 700-950) cases in the best scenario. Most cases and hospital admissions will involve patients aged 20 to 39 years, the number of deaths will be higher among the elderly and more pronounced among patients aged ≥80 years. Conclusion: this is the first study that provides COVID-19 projections for a municipality that is not a large capital. It shows a peak period at a later moment; therefore, the municipality will have more time to prepare and adopt protective measures to reduce the number of simultaneous cases.

RESUMEN Objetivo: obtener un modelo predictivo para la ocurrencia de casos, severidad y muertes por COVID-19 en Ponta Grossa-Paraná. Métodos: estudio ecológico con datos de casos confirmados de COVID-19 notificados del 21/03/2020 al 3/3/2020 en Ponta Grossa y proporción de severidad, hospitalización y letalidad en la literatura. Se construyó un modelo epidemiológico (SIR) infectado-recuperado susceptible y tasa de reproducción estimada (R0), duración de la epidemia, fecha pico, número de casos, hospitalizaciones y muertes. Este último por grupo de edad y en tres escenarios: a los 24 días, a los 34 días y a los 44 días de epidemia. Resultados: en los tres escenarios evaluados, la variación en el número de casos se explicó por una curva exponencial (r2 = 0.74, 0.79 y 0.89, respectivamente y p <0.0001 en total). El modelo SIR estimó que, en el mejor escenario, el pico ocurrirá alrededor de 120 días después del primer caso (entre el 7/11/2020 y el 25/7/2020), el R0 estimado será de 1.07 y alcanzará 0.23 % de habitantes infectados. En el peor de los casos, el pico estimado será de 4375 (IC del 95%: 4156-4594) y 825 (IC del 95%: 700-950) en el mejor de los casos. El mayor número estimado de casos y hospitalizaciones estará en el rango entre 20 y 39 años, el número de muertes será mayor entre los ancianos y más pronunciado entre ≥ 80 años. Conclusión: este es el primer estudio con proyecciones para COVID-19 en un municipio fuera de las grandes capitales y demostró que el pico llegará tarde, por lo tanto, el municipio tendrá más tiempo de preparación y que las medidas de protección pueden reducir el número simultáneo de casos.

RESUMO Objetivo: obter um modelo preditivo da ocorrência de casos, gravidade e óbitos por COVID-19 em Ponta Grossa-Paraná. Métodos: estudo ecológico com dados de casos confirmados de COVID-19 notificados de 21/03/2020 a 03/05/2020 em Ponta Grossa e proporção de gravidade, hospitalização e letalidade da literatura. Um modelo epidemiológico suscetível-infectado-recuperado (SIR) foi construído e estimadas taxa de reprodução (R0), duração da epidemia, data do pico, número de casos, hospitalizações e óbitos. Estas últimas por faixa etária e em três cenários: aos 24 dias, aos 34 dias e aos 44 dias de epidemia. Resultados: nos três cenários avaliados, a variação no número de casos foi explicada por uma curva exponencial (r2=0,74, 0,79 e 0,89, respectivamente e p<0,0001 em todos). O modelo SIR estimou que, no melhor cenário, o pico ocorrerá em torno de 120 dias após o primeiro caso (entre 11/07/2020 e 25/07/2020), o R0 estimado será 1,07 e chegará a 0,23% dos habitantes infectados. No pior cenário, o pico estimado será de 4375 (IC 95% 4156-4594) casos e 825 (IC 95% 700-950) no melhor cenário. O maior número estimado de casos e hospitalizações será na faixa entre 20 e 39 anos, o número de óbitos será maior entre idosos e mais acentuado entre ≥ 80 anos. Conclusão: este é o primeiro estudo com projeções para a COVID-19 em um município fora das grandes capitais e mostrou que o pico será tardio, portanto, o município terá mais tempo de preparo e que medidas protetivas podem reduzir o número simultâneo de casos.

Pandemia de Covid-19 y efecto de medidas de contención en población Peruana: Un modelamiento matemático SIR / Covid-19 pandemic and effect of containment measures in the Peruvian population: A SIR mathematical modeling

Introducción: La evolución de la pandemia del COVID-19 varía en cada población; complicando los sistemas de salud a nivel mundial. Objetivo: analizar la evolución de la pandemia Covid-19 estimando el efecto de las medidas de contención realizadas en Perú. Material y Métodos: Se aplicó el modelamiento matemático epidemiológico SIR, estimando la evolución COVID-19 en nuestra población. Se realizó el análisis de datos siguiendo el modelo matemático SIR con ecuaciones diferenciales ordinarias definidas para simular el comportamiento epidemiológico; y fue ejecutado en el lenguaje de programación RStudio. Resultados: En el estudio las medidas de contención disminuyeron la tasa de propagación, redujeron el 30% de casos infectados hasta el día pico de infección; sin embargo, ésta aún se encuentra por encima del número reproductivo efectivo para control de la epidemia y presenta una tendencia errática, el resultado de las acciones gubernamentales es del 61% en la práctica de medidas de contención. Conclusiones: Las medidas de contención son necesarias; siempre que, se consideren estrategias que permitan hacer efectivo su rol en nuestra población

Introduction: The evolution of the COVID-19 pandemic varies in each population; it has been complicating health systems worldwide. Objective: to analyze the evolution of the Covid-19 pandemic, estimating the effect of the containment measures practiced in Peru. Material and Method: The SIR epidemiological mathematical modeling was applied, estimating the COVID-19 evolution in our population. Data analysis was performed following the SIR mathematical model with defined ordinary differential equations to simulate epidemiological behavior; and it was executed in the RStudio programming language. Results: Containment measures decreased the propagation rate, reducing 30% of infected cases until the peak day of infection; however, it is still above the effective reproductive number to control the epidemic and it shows an erratic trend, the result of government actions being 61% in the practice of containment measures. Conclusions: Containment measures are necessary if strategies are considered to make their role effective in our population.

Mathematical model and COVID-19 / Modelos matemáticos y el COVID-19

Abstract Currently, there are several mathematical models that have been developed to understand the dynamics of COVID-19 infection. However, the difference in the sociocultural contexts between countries requires the specific adjustment of these estimates to each scenario. This article analyses the main elements used for the construction of models from epidemiological patterns, to describe the interaction, explain the dynamics of infection and recovery, and to predict possible scenarios that may arise with the introduction of public health measures such as social distancing and quarantines, specifically in the case of the pandemic unleashed by the new SARS-CoV-2/COVID-19 virus. Comment: Mathematical models are highly relevant for making objective and effective decisions to control and eradicate the disease. These models used for COVID-19 have supported and will continue to provide information for the selection and implementation of programs and public policies that prevent associated complications, reduce the speed of the virus spread and minimize the occurrence of severe cases of the disease that may collapse health systems.

Resumen En la actualidad existen varios modelos matemáticos que han sido desarrollados para entender la dinámica de la infección por COVID-19. Sin embargo, la diferencia en los contextos socioculturales entre países hace necesario el ajuste específico de estas estimaciones a cada escenario. Este artículo analiza los principales elementos usados para la construcción de los modelos a partir de patrones epidemiológicos, para lograr describir la interacción, explicar la dinámica de infección y recuperación, así como para predecir posibles escenarios que pueden presentarse con la introducción de medidas en salud pública como el distanciamiento social y cuarentenas, específicamente para el caso de la pandemia desatada por el nuevo virus SARS-CoV-2/COVID-19. Comentario: Los modelos matemáticos son de gran relevancia para la toma de decisiones objetivas y eficaces para controlar y erradicar la enfermedad. Estos modelos usados para el COVID-19, han apoyado y seguirán aportando información para la selección e implementación de programas y políticas públicas que prevengan complicaciones asociadas, disminuyan la velocidad de propagación del virus y minimicen la aparición de casos severos de enfermedad que puedan colapsar los sistemas de salud.

Understanding the COVID-19 prevention and control strategies and their appropriate applicability through the basics of epidemiology

The current article is about the background knowledge of corona, various epidemiological definitions and different strategies adopted to prevent and control corona infection. How the preventive measures are applied and what is epidemiological basis behind these measures is the core of the article. The article also mentioned the variations in mortality pattern and goes on defining important indicators as case-fatality ratio, deaths/1 lakh population and the relevance of both in the current situation of corona infection. In the article, important terms such as different types of cases in corona infection, basic reproduction number, effective reproduction number, and their epidemiological significance in corona infection, herd immunity, and herd immunity threshold are discussed. The importance of lockdown as a preventive measure, enforcement of epidemic disease act 1897 and its amendment, disaster management act 2005, social distancing, cough etiquette, and others are highlighted.

Modelo SIR de la pandemia de COVID-19 en Colombia / SIR model of the COVID-19 pandemic in Colombia

RESUMEN Objetivo Desarrollar un modelo SIR pronóstico de la pandemia de COVID-19 en el territorio colombiano. Métodos Se utilizó un modelo SIR con enfoque determinístico para pronosticar el desarrollo de la pandemia de COVID-19 en Colombia. Los estados considerados fueron susceptibles (S), infecciosos (i) y recuperados o fallecidos (R). Los datos poblacionales se obtuvieron del Departamento Administrativo Nacional de estadística (Proyecciones de Población 2018-2020, difundida en enero de 2020) y los datos sobre casos diarios confirmados de COVID-19 del Instituto Nacional de Salud. Se plantearon diferentes modelos variando el número básico de reproducción (R0). Resultados A partir de los casos reportados por el Ministerio de Salud se crearon cuatro ambientes o escenarios simulados en un modelo SIR epidemiológico, se extendieron las series de tiempo hasta el 30 de mayo, fecha probable del 99% de infección poblacional. Un R0 de 2 es la aproximación más cercana al comportamiento de la pandemia durante los primeros 15 días desde el reporte del caso 0, el peor escenario se daría en la primera semana de abril con un R0 igual a 3. Conclusiones Se hacen necesarias nuevas medidas de mitigación y supresión en las fases de contención y transmisión sostenida, como aumento de la capacidad diagnostica por pruebas y desinfección de zonas pobladas y hogares de aislamiento.(AU)

ABSTRACT Objective To develop a prognostic SIR model of the COVID-19 pandemic in Colombia. Materials and Methods A SIR model with a deterministic approach was used to forecast the development of the COVID-19 pandemic in Colombia. The states considered were susceptible (S), infectious (i) and recovered or deceased (R). Population data were obtained from the National Administrative Department of Statistics (DANE) - Population Projections 2018-2020, released in January 2020-, and data on daily confirmed cases of COVID-19 from the National Institute of Health. Different models were proposed varying the basic reproduction number (R0). Results Based on the cases reported by the Ministry of Health, 4 simulated environments were created in an epidemiological SIR model. The time series was extended until May 30, the probable date when 99% of the population will be infected. R0=2 is the basic reproduction number and the closest approximation to the behavior of the pandemic during the first 15 days since the first case report; the worst scenario would occur in the first week of April with R0=3. Conclusions Further mitigation and suppression measures are necessary in the containment and sustained transmission phases, such as increased diagnostic capacity through testing and disinfection of populated areas and homes in isolation.(AU)

Predicciones de un modelo SEIR para casos de COVID-19 en Cali, Colombia / Predictions of a SEIR model for COVID-19 cases in Cali-Colombia

RESUMEN Objetivo Predecir el número de casos de COVID-19 en la ciudad de Cali-Colombia mediante el desarrollo de un modelo SEIR. Métodos Se utilizó un modelo determinista compartimental SEIR considerando los estados: susceptibles (S), expuestos (E), infectados (I) y recuperados (R). Los parámetros del modelo fueron seleccionados de acuerdo a la revisión de literatura. En el caso de la tasa de letalidad, se usaron los datos de la Secretaría de Salud Municipal de Cali. Se plantearon varios escenarios teniendo en cuenta variaciones en el número básico de reproducción (R0) y en la tasa de letalidad; además, se comparó la predicción hasta el 9 de abril con los datos observados. Resultados A través del modelo SEIR se encontró que, con el número básico de reproducción más alto (2,6) y utilizando la letalidad calculada para la ciudad de 2,0%, el número máximo de casos se alcanzaría el primero de junio con 195 666 (prevalencia); sin embargo, al comparar los casos observados con los esperados, al inicio la ocurrencia observada estaba por encima de la proyectada; pero luego cambia la tendencia con una disminución marcada de la pendiente. Conclusiones Los modelos epidemiológicos SEIR son métodos muy utilizados para la proyección de casos en enfermedades infecciosas; sin embargo, se debe tener en cuenta que son modelos deterministas que pueden utilizar parámetros supuestos y podrían generar resultados imprecisos.(AU)

ABSTRACT Objective To predict the number of cases of COVID-19 in the city of Cali-Colombia through the development of a SEIR model. Methods A SEIR compartmental deterministic model was used considering the states: susceptible (S), exposed (E), infected (I) and recovered (R). The model parameters were selected according to the literature review, in the case of the case fatality rate data from the Municipal Secretary of Health were used. Several scenarios were considered taking into account variations in the basic number of reproduction (R0), and the prediction until april 9 was compared with the observed data. Results Through the SEIR model it was found that with the highest basic number of reproduction [2,6] and using the case fatality rate for the city of 2,0%, the maximum number of cases would be reached on June 1 with 195 666 (prevalence). However, when comparing the observed with the expected cases, at the beginning the observed occurrence was above the projected, but then the trend changes decreasing the slope. Conclusions SEIR epidemiological models are widely used methods for projecting cases in infectious diseases, however it must be taken into account that they are deterministic models that can use assumed parameters and could generate imprecise results.(AU)

Estimación del intervalo serial y número reproductivo básico para los casos importados de COVID-19 / Estimation of serial interval and basic reproductive number for imported cases of COVID-19

RESUMEN Objetivo Estimar el intervalo serial y el número básico de reproducción de COVID-19 entre casos importados durante la fase de contención en Pereira, Colombia, 2020. Método Se realizó un estudio cuantitativo para determinar algunos aspectos de la dinámica de transmisión de la COVID-19. Se utilizaron las entrevistas epidemiológicas de campo en los que se incluyeron 12 casos confirmados por laboratorio con PCR-RT para SARS-CoV-2 importados y sus correspondientes casos secundarios confirmados, entre los que estaban contactos familiares y sociales. Resultados Los intervalos seriales en la COVID-19 se ajustan a una distribución Gamma, con una media del intervalo serial de 3,8 días (± 2,7) y un R0 de 1,7 (IC 95% 1,06-2,7) inferior a lo encontrado en otras poblaciones con inicio del brote. Conclusiones Un intervalo serial inferior al periodo de incubación como el que se estimó en este estudio sugiere un periodo de transmisión presintomático que, según otras investigaciones, alcanza un pico promedio a los 3,8 días, hecho que sugiere que durante la investigación epidemiológica de campo la búsqueda de contactos estrechos se realice desde al menos 2 días antes del inicio de síntomas del caso inicial.(AU)

ABSTRACT Objective To estimate the serial interval and the basic reproduction number of COVID-19 between imported cases during the containment phase in Pereira-Colombia, 2020. Method A quantitative study was carried out to determine the transmission dynamics for COVID-19. Field epidemiological data were used, which included 12 laboratory-confirmed cases with RT-PCR for imported SARS-CoV-2 and their corresponding confirmed secondary cases, including family and social contacts. Results The serial intervals in COVID-19 fit a Gamma distribution, with a mean of the serial interval of 3.8 days (2.7) and an R0 of 1.7 (95% CI 1.06-2.7) lower than that found in other populations with onset of the outbreak. Conclusions A serial interval lower than the incubation period such as that estimated in this study, suggests a presymptomatic transmission period that according to other investigations reaches an average peak at 3.8 days, suggesting that during the field epidemiological investigation the search for contacts Narrowing is performed from at least 2 days before the onset of symptoms of the initial case.(AU)

Modelo SIR de la pandemia de COVID-19 en Colombia / SIR model of the COVID-19 pandemic in Colombia / Modelo SIR da pandemia de COVID-19 na Colômbia

RESUMEN Objetivo Desarrollar un modelo SIR pronóstico de la pandemia de COVID-19 en el territorio colombiano. Métodos Se utilizó un modelo SIR con enfoque determinístico para pronosticar el desarrollo de la pandemia de COVID-19 en Colombia. Los estados considerados fueron susceptibles (S), infecciosos (i) y recuperados o fallecidos (R). Los datos poblacionales se obtuvieron del Departamento Administrativo Nacional de estadística (Proyecciones de Población 2018-2020, difundida en enero de 2020) y los datos sobre casos diarios confirmados de COVID-19 del Instituto Nacional de Salud. Se plantearon diferentes modelos variando el número básico de reproducción (R0). Resultados A partir de los casos reportados por el Ministerio de Salud se crearon cuatro ambientes o escenarios simulados en un modelo SIR epidemiológico, se extendieron las series de tiempo hasta el 30 de mayo, fecha probable del 99% de infección poblacional. Un R0 de 2 es la aproximación más cercana al comportamiento de la pandemia durante los primeros 15 días desde el reporte del caso 0, el peor escenario se daría en la primera semana de abril con un R0 igual a 3. Conclusiones Se hacen necesarias nuevas medidas de mitigación y supresión en las fases de contención y transmisión sostenida, como aumento de la capacidad diagnostica por pruebas y desinfección de zonas pobladas y hogares de aislamiento.

ABSTRACT Objective To develop a prognostic SIR model of the COVID-19 pandemic in Colombia. Materials and Methods A SIR model with a deterministic approach was used to forecast the development of the COVID-19 pandemic in Colombia. The states considered were susceptible (S), infectious (i) and recovered or deceased (R). Population data were obtained from the National Administrative Department of Statistics (DANE) - Population Projections 2018-2020, released in January 2020-, and data on daily confirmed cases of COVID-19 from the National Institute of Health. Different models were proposed varying the basic reproduction number (R0). Results Based on the cases reported by the Ministry of Health, 4 simulated environments were created in an epidemiological SIR model. The time series was extended until May 30, the probable date when 99% of the population will be infected. R0=2 is the basic reproduction number and the closest approximation to the behavior of the pandemic during the first 15 days since the first case report; the worst scenario would occur in the first week of April with R0=3. Conclusions Further mitigation and suppression measures are necessary in the containment and sustained transmission phases, such as increased diagnostic capacity through testing and disinfection of populated areas and homes in isolation.

RESUMO OBJETIVO Desenvolver um modelo SIR prognóstico da pandemia de COVID-19 no território colombiano. MÉTODOS Um modelo SIR com abordagem determinística foi usado para prever o desenvolvimento da pandemia de COVID-19 na Colômbia. Os estados considerados foram suscetíveis (S), infecciosos (i) e recuperados ou falecidos (R). Os dados populacionais foram obtidos do Departamento Administrativo Nacional de Estatística (Projeções de População 2018-2020, divulgado em janeiro de 2020) e dados sobre casos confirmados diariamente de COVID-19 do Instituto Nacional de Saúde. Diferentes modelos foram propostos variando o número básico de reprodução (R 0 ). RESULTADOS Dos casos relatados pelo Ministério da Saúde, quatro ambientes ou cenários simulados foram criados em um modelo epidemiológico de RIS, as séries temporais foram estendidas até 30 de maio, data provável de 99% de infecção populacional. Um R 0 de 2 é a aproximação mais próxima do comportamento da pandemia durante os primeiros 15 dias a partir do relato do caso 0, o pior cenário ocorreria na primeira semana de abril com um R 0 igual a 3. CONCLUSÕES Novas medidas de mitigação e supressão são necessárias nas fases de contenção e transmissão sustentada, como aumento da capacidade de diagnóstico por testes e desinfecção de áreas povoadas e residências isoladas.

La ocurrencia de rebrotes de la COVID-19 y su relación con el número reproductivo

RESUMEN El peligro de la ocurrencia de endemia por la COVID-19 es una preocupación del gobierno y epidemiólogos cubanos, pero conocer alguna métrica que influya en su surgimiento es de gran utilidad para evitarla. El objetivo de este trabajo es demostrar mediante modelos dinámicos y teoría cualitaiva de ecuaciones diferenciales, cómo el número reproductivo básico Ro constituye una métrica que incide en la ocurrencia de estos eventos. Se empleó un modelo de tipo SIR con demografía adaptado a las condiciones de Cuba. Los resultados demostraron que se consigue dar respuesta, desde el punto de vista matemático, a las condiciones que pueden causar un rebrote de la enfermedad. Recomendamos mantener activadas las medidas epidemiológicas que se relacionan en este trabajo y que ayudan a mantener controlados los casos confirmados que aparezcan y evitar de esta manera posibles rebrotes.

ABSTRACT The danger of the occurrence of endemic COVID-19 worries the Cuban government as well as epidemiologists. Knowledge about a metric that influences its emergence is a very useful tool to prevent it. The purpose of the study was to prove through dynamic models and the qualitative theory of differential equations that the basic reproduction number R0 is a metric influencing the occurrence of these events. A SIR model was used, which was adjusted to Cuban conditions. Results showed that a mathematical response may be provided to conditions potentially causing a fresh outbreak of the disease. We recommend to maintain activated the epidemiological measures referred to in the paper, which help keep under control the confirmed cases occurring, thus preventing possible fresh outbreaks.

Estimating the basic reproduction number of COVID-19 in Wuhan, China / 中华流行病学杂志

Objective@#The number of confirmed and suspected cases of the COVID-19 in Hubei province is still increasing. However, the estimations of the basic reproduction number of COVID-19 varied greatly across studies. The objectives of this study are 1) to estimate the basic reproduction number (R0) of COVID-19 reflecting the infectiousness of the virus and 2) to assess the effectiveness of a range of controlling intervention.@*Method@#The reported number of daily confirmed cases from January 17 to February 8, 2020 in Hubei province were collected and used for model fit. Four methods, the exponential growth (EG), maximum likelihood estimation (ML), sequential Bayesian method (SB) and time dependent reproduction numbers (TD), were applied to estimate the R0.@*Result@#Among the four methods, the EG method fitted the data best. The estimated R0 was 3.49 (95% CI: 3.42-3.58) by using EG method. The R0 was estimated to be 2.95 (95%CI: 2.86-3.03) after taking control measures.@*Conclusion@#In the early stage of the epidemic, it is appropriate to estimate R0 using the EG method. Meanwhile, timely and effective control measures were warranted to further reduce the spread of COVID-19.

Study on assessing early epidemiological parameters of coronavirus disease epidemic in China / 中华流行病学杂志

Objective@#To study the early dynamics of the epidemic of coronavirus disease (COVID-19) in China from 15 to 31 January, 2020, and estimate the corresponding epidemiological parameters (incubation period, generation interval and basic reproduction number) of the epidemic.@*Methods@#By means of Weibull, Gamma and Lognormal distributions methods, we estimated the probability distribution of the incubation period and generation interval data obtained from the reported COVID-19 cases. Moreover, the AIC criterion was used to determine the optimal distribution. Considering the epidemic is ongoing, the exponential growth model was used to fit the incidence data of COVID-19 from 10 to 31 January, 2020, and exponential growth method, maximum likelihood method and SEIR model were used to estimate the basic reproduction number.@*Results@#Early COVID-19 cases kept an increase in exponential growth manner before 26 January, 2020, then the increase trend became slower. The average incubation period was 5.01 (95%CI: 4.31-5.69) days; the average generation interval was 6.03 (95%CI: 5.20-6.91) days. The basic reproduction number was estimated to be 3.74 (95%CI: 3.63-3.87), 3.16 (95%CI: 2.90-3.43), and 3.91 (95%CI: 3.71-4.11) by three methods, respectively.@*Conclusions@#The Gamma distribution fits both the generation interval and incubation period best, and the mean value of generation interval is 1.02 day longer than that of incubation period. The relatively high basic reproduction number indicates that the epidemic is still serious; Based on our analysis, the turning point of the epidemic would be seen on 26 January, the growth rate would be lower afterwards.

Estimating the basic reproduction number of COVID-19 in Wuhan, China / 中华流行病学杂志

Objective The number of confirmed and suspected cases of the COVID-19 in Hubei province is still increasing. However, the estimations of the basic reproduction number of COVID-19 varied greatly across studies. The objectives of this study are 1) to estimate the basic reproduction number ( R 0 ) of COVID-19 reflecting the infectiousness of the virus and 2) to assess the effectiveness of a range of controlling intervention. Method The reported number of daily confirmed cases from January 17 to February 8, 2020 in Hubei province were collected and used for model fit. Four methods, the exponential growth (EG), maximum likelihood estimation (ML), sequential Bayesian method (SB) and time dependent reproduction numbers (TD), were applied to estimate the R 0 . Result Among the four methods, the EG method fitted the data best. The estimated R 0 was 3.49 (95% CI : 3.42-3.58) by using EG method. The R 0 was estimated to be 2.95 (95% CI : 2.86-3.03) after taking control measures. Conclusion In the early stage of the epidemic, it is appropriate to estimate R 0 using the EG method. Meanwhile, timely and effective control measures were warranted to further reduce the spread of COVID-19.

Pay attention to situation of SARS-CoV-2 and TCM advantages in treatment of novel coronavirus infection / 中草药·英文版

Since the outbreak of the new coronavirus epidemic, novel coronavirus has infected nearly 100,000 people in more than 110 countries. How to face this new coronavirus epidemic outbreak is an important issue. Basic reproduction number (R0) is an important parameter in epidemiology; The basic reproduction number of an infection can be thought of as the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. Epidemiology dynamics is a mathematical model based on a susceptibility-infection-recovery epidemic model. Researchers analyzed the epidemiological benefits of different transmission rates for the establishment of effective strategy in prevention and control strategies for epidemic infectious diseases. In this review, the early use of TCM for light and ordinary patients, can rapidly improve symptoms, shorten hospitalization days and reduce severe cases transformed from light and normal. Many TCM formulas and products have wide application in treating infectious and non-infectious diseases. The TCM theoretical system of treating epidemic diseases with TCM and the treatment scheme of integrated Chinese and Western medicine have proved their effectiveness in clinical practice. TCM can cure COVID-19 pneumonia, and also shows that the role of TCM in blocking the progress of COVID-19 pneumonia.

Estimando el efecto del cambio climático sobre el riesgo de la enfermedad de Chagas en Chile por medio del número reproductivo / Effects of climate change on reproductive number of Chagas disease

Background: Reproductive number (R0)-maps estimate risk zones of vector-borne diseases and geographical distribution changes under climate change. Aim: To map R0 aiming to estimate the epidemiological risk of Chagas disease in Chile, its distribution and possible changes due to the global climate change. Material and Methods: We used a relationship between R0 and entomological parameters of vectors as function of environmental variables, to map the risk of Chagas disease in Chile, under current and projected future environmental conditions. Results: We obtained a geographical R0 estimation of Chagas disease in Chile. The highest R0averages correspond to the Central-Northern regions of Chile. T. cruzi transmission area could increase in the future due to climate changes. Independent of the future condition, both for optimistic and pessimistic climate change scenarios, the area of potential risk for Chagas disease transmission would increase. The estimated R0 values suggest that, if a control of T. infestans is not maintained, Chagas disease endemic status will persist or increase, independently of the climate change scenarios. Conclusions: Mapping R0 values is an effective method to assess the risk of Chagas disease. The eventual increase in the transmission area of the disease is worrisome.

A dynamic model of hand foot and mouth disease in Jiangsu Province based on EV71 vaccination / 中华疾病控制杂志

Objective To establish a dynamic model of hand foot and mouth disease in Jiangsu Province, analyze the epidemic of hand foot and mouth disease in Jiangsu, predict the trend of this disease and simulate the effect of EV71 vaccination on the control of hand foot and mouth disease caused by EV71. Methods A compartmental model of hand foot and mouth disease was constructed.A group of differential equations was established. The incidence data of hand foot and mouth disease was used to fit the model and calculate the basic reproduction number of this disease in Jiangsu. Then, vaccination was added to the model and the incidence of hand foot and mouth disease under different vaccination coverage rates was simulated. Results The basic reproduction numbers of hand foot and mouth disease in Jiangsu between 2013 and 2016 were 1.31 (IQR:0.99-1.48), 1.37 (IQR:0.97-1.52), 1.34 (IQR:1.00-1.61) and 1.38 (IQR:1.00-1.76) , respectively. With the increase of immunization coverage of EV71 vaccine, the cases of hand foot and mouth disease caused by EV71 decreased accordingly. When the annual immunization rate of EV71 vaccine was maintained at a high level (75%), the annual incidence of hand foot and mouth disease caused by EV71 after 5 years reduced to 10% of that in the same year when there was no vaccination. Conclusions The epidemic trend of hand foot and mouth disease in Jiangsu is stable from 2013 to 2016. Vaccination plays an important role in controlling hand foot and mouth disease caused by EV71.

Data Fitting and Scenario Analysis of Vaccination in the 2014 Ebola Outbreak in Liberia

OBJECTIVES: This study aimed to extend an epidemiological model (SEIHFR) to analyze epidemic trends, and evaluate intervention efficacy. METHODS: SEIHFR was modified to examine disease transmission dynamics after vaccination for the Ebola outbreak. Using existing data from Liberia, sensitivity analysis of various epidemic scenarios was used to inform the model structure, estimate the basic reproduction number ℜ₀ and investigate how the vaccination could effectively change the course of the epidemic. RESULTS: If a randomized mass vaccination strategy was adopted, vaccines would be administered prophylactically or as early as possible (depending on the availability of vaccines). An effective vaccination rate threshold for Liberia was estimated as 48.74% among susceptible individuals. If a ring vaccination strategy was adopted to control the spread of the Ebola virus, vaccines would be given to reduce the transmission rate improving the tracing rate of the contact persons of an infected individual. CONCLUSION: The extended SEIHFR model predicted the total number of infected cases, number of deaths, number of recoveries, and duration of outbreaks among others with different levels of interventions such as vaccination rate. This model may be used to better understand the spread of Ebola and develop strategies that may achieve a disease-free state.

Modification of the Conventional Influenza Epidemic Models Using Environmental Parameters in Iran / 대한의료정보학회지

OBJECTIVES: The association between the spread of infectious diseases and climate parameters has been widely studied in recent decades. In this paper, we formulate, exploit, and compare three variations of the susceptible-infected-recovered (SIR) model incorporating climate data. The SIR model is a well-studied model to investigate the dynamics of influenza viruses; however, the improved versions of the classic model have been developed by introducing external factors into the model. METHODS: The modification models are derived by multiplying a linear combination of three complementary factors, namely, temperature (T), precipitation (P), and humidity (H) by the transmission rate. The performance of these proposed models is evaluated against the standard model for two outbreak seasons. RESULTS: The values of the root-mean-square error (RMSE) and the Akaike information criterion (AIC) improved as they declined from 8.76 to 7.05 and from 98.12 to 93.01 for season 2013/14, respectively. Similarly, for season 2014/15, the RMSE and AIC decreased from 8.10 to 6.45 and from 117.73 to 107.91, respectively. The estimated values of R(t) in the framework of the standard and modified SIR models are also compared. CONCLUSIONS: Through simulations, we determined that among the studied environmental factors, precipitation showed the strongest correlation with the transmission dynamics of influenza. Moreover, the SIR+P+T model is the most efficient for simulating the behavioral dynamics of influenza in the area of interest.

An investigation of a measles outbreak in Japan and Taiwan, China, March–May 2018

Objective@#To investigate a measles outbreak that spread to Japan and Taiwan, China during March–May 2018, exploring the characteristics of the super-spreading event.@*Methods@#A contact investigation of the index case and reconstruction of the epidemiological dynamics of measles transmission were conducted. Employing a mathematical model, the effective reproduction number was estimated for each generation of cases.@*Results and discussion@#A single index case gave rise to a total of 38 secondary cases, 33 in Japan and five in Taiwan, China. Subsequent chains of transmission were observed in highly vaccinated populations in both Japan and Taiwan, China. The effective reproduction number of the second generation was >1 for both Japan and Taiwan, China. In Japan, the reproduction number was estimated to be <1 during the third generation. Vaccination of susceptible individuals is essential to prevent secondary and tertiary transmission events.

Application of State Space model in the evaluation of the prevention and control for mumps / 中华流行病学杂志

Objective To analyze the epidemiological characteristics of mumps in 2012 and 2014,and to explore the preventive effect of the second dose of mumps-containing vaccine (MuCV) in mumps in Shandong province.Methods On the basis of certain model assumptions,a Space State model was formulated.Iterated Filter was applied to the epidemic model to estimate the parameters.Results The basic reproduction number (R0) for children in schools was 4.49 (95％ CI:4.30-4.67)and 2.50 (95％CI:2.38-2.61) respectively for the year of 2012 and 2014.Conclusions Space State model seems suitable for mumps prevalence description.The policy of 2-dose MuCV can effectively reduce the number of total patients.Children in schools are the key to reduce the mumps.