Mathematical modelling approach of the study of Ebola virus disease transmission dynamics in a developing country

Background: Ebola Virus causes disease both in human and non-human primatesespecially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date. Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus ina population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle.Results: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.

Assessment of COVID-19 Omicron epidemic trend in Shanghai based on time-varying reproduction number / 上海预防医学

ObjectiveTo assess the epidemic trend of COVID-19 Omicron and the effectiveness of containment measures in Shanghai by estimating the time-varying reproduction number （Rt）. MethodsBased on the daily reported confirmed cases and asymptomatic infections in Shanghai from February 20 to April 26， 2022， the R package "Epiestim"， which was built by Bayesian framework method， was used to estimate the variation curve of Rt during the epidemic period and to analyze the trend of the epidemic. ResultsIn the early stage of the epidemic， after the implementation of school closure and nuclear acid screening in some communities， Rt continued to fluctuate between 2.000 and 3.000， reaching a peak of 2.740 （95%CI： 2.640‒2.830） on March 21， but began to decline around one week after the city lock-down on April 1. As of April 18， the Rt value in Shanghai was below the threshold of 1.000 for the first time， reaching 0.955 （95%CI： 0.951‒0.961）. ConclusionAfter the implementation of public health measures with increasing strength of containment in Shanghai， the transmission rate gradually decreased， reflecting the effectiveness of the interventions. In the actual prevention and control process， the containment work should not be relaxed in order to keep the Rt below 1.000.

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.

Assessment of the global status of COVID-19 epidemics / 公共卫生与预防医学

Objective To analyze the global status of COVID-19 epidemics, so as to preliminarily forecast the epidemic trend. Methods The epidemiological data of 208 countries and the prevention and control policies implemented by typical countries from December 31, 2019 to December 14, 2020 were collected. We use the cumulative incidence rate, cumulative mortality, cumulative fatality and real-time dependent reproduction number (Rt) to analyze the epidemic status. We use the provenance package to group different countries and discuss the effect of prevention and control measures. Results As of December 14, 2020, a cumulative incidence of 93.49 per 10000, a cumulative mortality rate of 0.21‰, and a cumulative fatality rate of 3.1‰ had been reported globally.112 of the 208 countries still had Rt ≥ 1.0, and 96 countries had Rt t , and the government had adopted more relaxed epidemic prevention measures. The epidemic situation in this region may continue to deteriorate, and needs to be focused in the later period.

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.

Estimación del número reproductivo efectivo del brote de sarampión 2018-2019 en Chile / Estimation of the effective reproduction number of measles 2018-2019 in Chile

Resumen Introducción: Los casos de sarampión están resurgiendo en muchos países del mundo. Hubo un brote de sarampión importado entre noviembre de 2018 y febrero de 2019 en Chile, lo que generó preocupación entre el público y las autoridades sanitarias. Muchos se preocuparon por la tasa de inmunización contra el sarampión de la población, un factor que se relaciona con la capacidad reproductiva del virus (medida de transmisibilidad de un patógeno). Objetivo: Aquí estimamos el número reproductivo efectivo (Re) de este brote de sarampión. Resultados: Aunque la estimación tiene mucha incertidumbre por el bajo número de casos y la ausencia de mezcla homogénea de la población, encontramos que Re fue aproximadamente 1,5. Discusión y Conclusiones: En consecuencia estimamos que aproximadamente 90,3% de la población tiene inmunidad al sarampión, lo que coincide con las estimaciones del Ministerio de Salud. Estos resultados sugieren que la población chilena ha establecido la inmunidad colectiva contra la introducción de casos importados de sarampión, lo que refleja un manejo preventivo adecuado de esta enfermedad.

Abstract Background: Measles cases are reemerging in many countries across the globe. There was an outbreak of imported measles between November 2018 and February 2019 in Chile, raising concern among the public and health authorities. Many were worried about the Chilean measles herd immunity, a factor that relates to the reproductive capacity of the virus (measure of transmissibility of a pathogen). Aim: Here we estimate the effective reproductive number (Re) of this measles outbreak. Results: Although the estimate is highly uncertain due to the low number of cases and the absence of homogeneous mixing of the population, we found Re was approximately 1.5. Discussion and Conclusions: Consequently we estimated about 90,3 % had measles immunity, consistent with administrative estimates from the Ministry of Health. These results suggest the Chilean population has established herd immunity against the introduction of imported measles cases, reflecting adequate preventive management of this disease.

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.

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

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)

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.

Epidemic trend of COVID-19 in some high--epidemic countries / 预防医学

Objeetive@#To learn the epidemic status of COVID-19 in some high-epidemic countries, so as to provide reference for prevention and control of imported COVID-19 in China. @*Methods@#We collected the data of all the countries who totally reported over ten thousand cases of COVID-19 by March 29, 2020, and analyzed the epidemic trend by using the incidence rate, the case fatality rate, the five-day moving average time dependent reproduction number (Rt) as well as the average daily increase rate. @*Results @#Spain, Switzerland, Italy, Germany, France, lran, UK, USA and China were inchuded in the analysis. Spain( 15.46/100 000), Switzerland(15.44/100 000) and Italy ( 15.30/100 000)ranked top three in the incidence rate of COVID-19. Italy (10.84%), Spain (7.88%) andlan (7.11%) ranked top three in the case atality rate. By March27, the values of five-day moving average Rt in USA, UK, Iran, Spain and France were all more than one. The average daily increase rate in China had changed negative since March 6. The average daily increase rates in the other eight countries ranged from 41.58% to 18.17%, and the trend was slow down from March 20 to 29, among which Germany, Switzerland and Italy had the largest decline of 35.60%, 29.76% and 25.56%, respectively @*Conclusions @#By March 29, the epidemie situation of COVID-19 in China was under controls; the situations in ltaly, Germany and Switzerland tended to be stable; while the situations in USA, UK, Iran, Spain and France maintained an upward tmend.

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.

Fitting prediction of transmissibility and incidence trend of novel coronavirus pneumonia in Ningxia / 公共卫生与预防医学

Objective To analyze the change in transmissibility of novel coronavirus pneumonia and predict the trend of the incidence, and to provide a reference for the government to better respond to the novel coronavirus pneumonia epidemic. Methods The EpiEstimof R language software was used to estimate the change of effective basic reproduction number, and the Richards model was run by Matlab7.0 software to fit the cumulative number of confirmed cases and the number of suspected cases. The coefficient of determination and root mean squared error were used to evaluate the fitting effect of the model. Results A total of 75 confirmed cases and 107 suspected cases were reported in Ningxia. The strict implementation of various prevention and control measures gradually reduced the effective basic reproduction number from 3.82 to less than 1, indicating that the epidemic was under control. The Richards model was used to fit the cumulative confirmed cases and suspected cases, which revealed that the natural growth rates were 0.16 and 0.23, and the coefficients of determination were 0.991 and 0.998, respectively. Conclusion Combined with the effective basic reproduction number, the Richards model fitted the trend of novel coronavirus pneumonia, which can be used to predict the trend of incidence of new coronavirus pneumonia.

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.

Dynamic basic reproduction number based evaluation for current prevention and control of COVID-19 outbreak in China / 中华流行病学杂志

Objective@#To evaluate the current status of the prevention and control of coronavirus disease (COVID-19) outbreak in China, establish a predictive model to evaluate the effects of the current prevention and control strategies, and provide scientific information for decision- making departments.@*Methods@#Based on the epidemic data of COVID-19 openly accessed from national health authorities, we estimated the dynamic basic reproduction number R0(t) to evaluate the effects of the current COVID-19 prevention and control strategies in all the provinces (municipalities and autonomous regions) as well as in Wuhan and the changes in infectivity of COVID-19 over time.@*Results@#For the stability of the results, 24 provinces (municipality) with more than 100 confirmed COVID-19 cases were included in the analysis. At the beginning of the outbreak, the R0(t) showed unstable trend with big variances. As the strengthening of the prevention and control strategies, R0(t) began to show a downward trend in late January, and became stable in February. By the time of data analysis, 18 provinces (municipality) (75%) had the R0(t)s less than 1. The results could be used for the decision making to free population floating conditionally.@* Conclusions@#Dynamic R0(t) is useful in the evaluation of the change in infectivity of COVID-19, the prevention and control strategies for the COVID-19 outbreak have shown preliminary effects, if continues, it is expected to control the COVID-19 outbreak in China in near future.