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In this paper we examine several definitions of vaccine efficacy (VE) that we found in the literature, for diseases that express themselves in outbreaks, that is, when the force of infection grows in time, reaches a maximum and then vanishes. The fact that the disease occurs in outbreaks results in several problems that we analyse. We propose a mathematical model that allows the calculation of VE for several scenarios. Vaccine trials usually needs a large number of volunteers that must be enrolled. Ideally, all volunteers should be enrolled in approximately the same time, but this is generally impossible for logistic reasons and they are enrolled in a fashion that can be replaced by a continuous density function (for example, a Gaussian function). The outbreak can also be replaced by a continuous density function, and the use of these density functions simplifies the calculations. Assuming, for example Gaussian functions, one of the problems one can immediately notice is that the peak of the two curves do not occur at the same time. The model allows us to conclude: First, the calculated vaccine efficacy decreases when the force of infection increases; Second, the calculated vaccine efficacy decreases when the gap between the peak in the force of infection and the peak in the enrollment rate increases; Third, different trial protocols can be simulated with this model; different vaccine efficacy definitions can be calculated and in our simulations, all result are approximately the same. The final, and perhaps most important conclusion of our model, is that vaccine efficacy calculated during outbreaks must be carefully examined and the best way we can suggest to overcome this problem is to stratify the enrolled volunteer's in a cohort-by-cohort basis and do the survival analysis for each cohort, or apply the Cox proportional hazards model for each cohort.
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Background: Household transmission studies seek to understand the transmission dynamics of a pathogen by estimating the risk of infection from household contacts and community exposures. We estimated within/extra-household SARS-CoV-2 infection risk and associated factors in a household cohort study in one of the most vulnerable neighbourhoods in Rio de Janeiro city. Methods: Individuals ≥1 years-old with suspected or confirmed COVID-19 in the past 30 days (index cases) and household members aged ≥1 year were enrolled and followed at 14 and 28 days (study period November/2020-December/2021). RT-PCR testing, COVID-19 symptoms, and SARS-CoV-2 serologies were ascertained in all visits. Chain binomial household transmission models were fitted using data from 2024 individuals (593 households). Findings: Extra-household infection risk was 74.2% (95% credible interval [CrI] 70.3-77.8), while within-household infection risk was 11.4% (95% CrI 5.7-17.2). Participants reporting having received two doses of a COVID-19 vaccine had lower extra-household (68.9%, 95% CrI 57.3-77.6) and within-household (4.1%, 95% CrI 0.4-16.6) infection risk. Within-household infection risk was higher among participants aged 10-19 years, from overcrowded households, and with low family income. Contrastingly, extra-household infection risk was higher among participants aged 20-29 years, unemployed, and public transportation users. Interpretation: Our study provides important insights into COVID-19 household/community transmission in a vulnerable population that resided in overcrowded households and who struggled to adhere to lockdown policies and social distancing measures. The high extra-household infection risk highlights the extreme social vulnerability of this population. Prioritising vaccination of the most socially vulnerable could protect these individuals and reduce widespread community transmission. Funding: Fundação Oswaldo Cruz, CNPq, FAPERJ, Royal Society, Instituto Serrapilheira, FAPESP.
RESUMO
In this paper we examine several definitions of vaccine efficacy (VE) that we found in the literature, for diseases that express themselves in outbreaks, that is, when the force of infection grows in time, reaches a maximum and then vanishes. The fact that the disease occurs in outbreaks results in several problems that we analyse. We propose a mathematical model that allows the calculation of VE for several scenarios. Vaccine trials usually needs a large number of volunteers that must be enrolled. Ideally, all volunteers should be enrolled in approximately the same time, but this is generally impossible for logistic reasons and they are enrolled in a fashion that can be replaced by a continuous density function (for example, a Gaussian function). The outbreak can also be replaced by a continuous density function, and the use of these density functions simplifies the calculations. Assuming, for example Gaussian functions, one of the problems one can immediately notice is that the peak of the two curves do not occur at the same time. The model allows us to conclude: First, the calculated vaccine efficacy decreases when the force of infection increases; Second, the calculated vaccine efficacy decreases when the gap between the peak in the force of infection and the peak in the enrollment rate increases; Third, different trial protocols can be simulated with this model; different vaccine efficacy definitions can be calculated and in our simulations, all result are approximately the same. The final, and perhaps most important conclusion of our model, is that vaccine efficacy calculated during outbreaks must be carefully examined and the best way we can suggest to overcome this problem is to stratify the enrolled volunteer's in a cohort-by-cohort basis and do the survival analysis for each cohort, or apply the Cox proportional hazards model for each cohort
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BACKGROUND: After validation in multiple types of liver disease patients, the MELD score was adopted as a standard by which liver transplant candidates with end-stage liver disease were prioritized for organ allocation in the United States since 2002, and in Brazil, since 2006. AIMS: To analyze the mortality profile of patients on the liver transplant waiting list correlated to MELD score at the moment of transplantation. METHODS: This study used the data from the Secretary of Health of the São Paulo State, Brazil, which listed 22,522 patients, from 2006 (when MELD score was introduced in Brazil) until June 2009. Patients with acute hepatic failure and tumors were included as well. We also considered the mortality of both non-transplanted and transplanted patients as a function of the MELD score at presentation. RESULTS: Our model showed that the best MELD score for patients on the liver transplant waiting list associated to better results after liver transplantation was 26. CONCLUSIONS: We found that the best score for applying to liver transplant waiting list in the State of São Paulo was 26. This is the score that minimizes the mortality in both non-transplanted and liver transplanted patients.
Assuntos
Doença Hepática Terminal , Transplante de Fígado , Humanos , Brasil , Listas de Espera , Doença Hepática Terminal/cirurgiaRESUMO
Objective: To assess how relevant the flow of people between communities is, compared to vaccination and type of vector, on the spread and potential outbreaks of yellow fever in a disease-free host community. Methods: Using a SEIRV-SEI model for humans and vectors, we applied numerical simulations to the scenarios: (1) migration from an endemic community to a disease-free host community, comparing the performance of Haemagogus janthinomys and Aedes aegypti as vectors; (2) migration through a transit community located on a migratory route, where the disease is endemic, to a disease-free one; and (3) effects of different vaccination rates in the host community, considering the vaccination of migrants upon arrival. Results: Results show no remarkable differences between scenarios 1 and 2. The type of vector and vaccination coverage in the host community are more relevant for the occurrence of outbreaks than migration rates, with H. janthinomys being more effective than A. aegypti. Conclusions: With vaccination being more determinant for a potential outbreak than migration rates, vaccinating migrants on arrival may be one of the most effective measures against yellow fever. Furthermore, H. janthinomys is a more competent vector than A. aegypti at similar densities, but the presence of A. aegypti is a warning to maintain vaccination above recommended levels.
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[ABSTRACT]. Objective. To assess how relevant the flow of people between communities is, compared to vaccination and type of vector, on the spread and potential outbreaks of yellow fever in a disease-free host community. Methods. Using a SEIRV-SEI model for humans and vectors, we applied numerical simulations to the scenarios: (1) migration from an endemic community to a disease-free host community, comparing the performance of Haemagogus janthinomys and Aedes aegypti as vectors; (2) migration through a transit community located on a migratory route, where the disease is endemic, to a disease-free one; and (3) effects of different vaccination rates in the host community, considering the vaccination of migrants upon arrival. Results. Results show no remarkable differences between scenarios 1 and 2. The type of vector and vaccination coverage in the host community are more relevant for the occurrence of outbreaks than migration rates, with H. janthinomys being more effective than A. aegypti. Conclusions. With vaccination being more determinant for a potential outbreak than migration rates, vac- cinating migrants on arrival may be one of the most effective measures against yellow fever. Furthermore, H. janthinomys is a more competent vector than A. aegypti at similar densities, but the presence of A. aegypti is a warning to maintain vaccination above recommended levels.
[RESUMEN]. Objetivo. Evaluar la importancia del flujo de personas entre comunidades, en comparación con la vacunación y el tipo de vector, para la propagación y los posibles brotes de fiebre amarilla en una comunidad de acogida libre de la enfermedad. Métodos. Con el empleo de un modelo SEIRV—SEI para personas y vectores, aplicamos simulaciones numéricas a las siguientes situaciones hipotéticas: 1) migración desde una comunidad con endemicidad a una comunidad de acogida libre de la enfermedad, en la que se compararon los resultados producidos por Haemagogus janthinomys y Aedes aegypti como vectores; 2) migración a través de una comunidad de tránsito situada en una ruta migratoria, donde la enfermedad es endémica, hacia otra comunidad libre de la enfermedad; y 3) efectos de tasas de vacunación diferentes en la comunidad de acogida, tomando en consideración la vacunación de las personas migrantes a su llegada. Resultados. Los resultados no muestran diferencias notables entre las situaciones 1 y 2. En cuanto a la aparición de brotes, tanto la cobertura vacunal en la comunidad de acogida como el tipo de vector tienen más importancia que las tasas de migración; y H. janthinomys muestra mayor eficacia que A. aegypti. Conclusiones. Dado que, para determinar la aparición de un posible brote, la vacunación tiene mayor importancia que las tasas de migración, la vacunación de las personas migrantes a su llegada puede ser una de las medidas más eficaces contra la fiebre amarilla. Además, a densidades similares, H. janthinomys es un vector más competente que A. aegypti, por lo que la presencia de A. aegypti constituye una señal de alerta para mantener la vacunación por encima de los niveles recomendados.
[RESUMO]. Objetivo. Avaliar a relevância do fluxo de pessoas entre comunidades em comparação com a vacinação e tipo de vetor para a propagação e potenciais surtos de febre amarela em uma comunidade de destino livre da doença. Métodos. Usando um modelo SEIRV-SEI para humanos e vetores, foram aplicadas simulações numéricas aos seguintes cenários: (1) migração de uma comunidade endêmica para uma comunidade de destino livre da doença, comparando o desempenho de Haemagogus janthinomys e de Aedes aegypti como vetores; (2) migração através de uma comunidade de trânsito localizada em uma rota migratória, onde a doença é endêmica, para uma comunidade de destino livre da doença; e (3) efeitos de diferentes taxas de vacinação na comunidade de destino, considerando-se a vacinação dos migrantes ao chegarem. Resultados. Os resultados não revelaram diferenças marcantes entre os cenários 1 e 2. O tipo de vetor e a cobertura vacinal na comunidade de destino são mais relevantes para a ocorrência de surtos do que as taxas de migração; o vetor H. janthinomys é mais efetivo do que A. aegypti. Conclusões. Na medida em que a vacinação é mais determinante para um potencial surto que as taxas de migração, a vacinação de migrantes na chegada pode ser uma das medidas mais efetivas contra a febre amarela. Além disso, o H. janthinomys é um vetor mais competente do que o A. aegypti em densidades similares, mas a presença de A. aegypti é um alerta para manter a vacinação acima dos níveis recomendados.
Assuntos
Febre Amarela , Vacinação , Migração Humana , Modelos Epidemiológicos , Saúde Pública , Doenças Transmitidas por Vetores , Surtos de Doenças , América Latina , Febre Amarela , Vacinação , Migração Humana , Modelos Epidemiológicos , Saúde Pública , Doenças Transmitidas por Vetores , Surtos de Doenças , América Latina , Febre Amarela , Vacinação , Migração Humana , Saúde Pública , Doenças Transmitidas por Vetores , Surtos de DoençasRESUMO
In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.
Assuntos
COVID-19 , Humanos , COVID-19/prevenção & controle , SARS-CoV-2 , Eficácia de Vacinas , Surtos de DoençasRESUMO
ABSTRACT Objective. To assess how relevant the flow of people between communities is, compared to vaccination and type of vector, on the spread and potential outbreaks of yellow fever in a disease-free host community. Methods. Using a SEIRV-SEI model for humans and vectors, we applied numerical simulations to the scenarios: (1) migration from an endemic community to a disease-free host community, comparing the performance of Haemagogus janthinomys and Aedes aegypti as vectors; (2) migration through a transit community located on a migratory route, where the disease is endemic, to a disease-free one; and (3) effects of different vaccination rates in the host community, considering the vaccination of migrants upon arrival. Results. Results show no remarkable differences between scenarios 1 and 2. The type of vector and vaccination coverage in the host community are more relevant for the occurrence of outbreaks than migration rates, with H. janthinomys being more effective than A. aegypti. Conclusions. With vaccination being more determinant for a potential outbreak than migration rates, vaccinating migrants on arrival may be one of the most effective measures against yellow fever. Furthermore, H. janthinomys is a more competent vector than A. aegypti at similar densities, but the presence of A. aegypti is a warning to maintain vaccination above recommended levels.
RESUMEN Objetivo. Evaluar la importancia del flujo de personas entre comunidades, en comparación con la vacunación y el tipo de vector, para la propagación y los posibles brotes de fiebre amarilla en una comunidad de acogida libre de la enfermedad. Métodos. Con el empleo de un modelo SEIRV—SEI para personas y vectores, aplicamos simulaciones numéricas a las siguientes situaciones hipotéticas: 1) migración desde una comunidad con endemicidad a una comunidad de acogida libre de la enfermedad, en la que se compararon los resultados producidos por Haemagogus janthinomys y Aedes aegypti como vectores; 2) migración a través de una comunidad de tránsito situada en una ruta migratoria, donde la enfermedad es endémica, hacia otra comunidad libre de la enfermedad; y 3) efectos de tasas de vacunación diferentes en la comunidad de acogida, tomando en consideración la vacunación de las personas migrantes a su llegada. Resultados. Los resultados no muestran diferencias notables entre las situaciones 1 y 2. En cuanto a la aparición de brotes, tanto la cobertura vacunal en la comunidad de acogida como el tipo de vector tienen más importancia que las tasas de migración; y H. janthinomys muestra mayor eficacia que A. aegypti. Conclusiones. Dado que, para determinar la aparición de un posible brote, la vacunación tiene mayor importancia que las tasas de migración, la vacunación de las personas migrantes a su llegada puede ser una de las medidas más eficaces contra la fiebre amarilla. Además, a densidades similares, H. janthinomys es un vector más competente que A. aegypti, por lo que la presencia de A. aegypti constituye una señal de alerta para mantener la vacunación por encima de los niveles recomendados.
RESUMO Objetivo. Avaliar a relevância do fluxo de pessoas entre comunidades em comparação com a vacinação e tipo de vetor para a propagação e potenciais surtos de febre amarela em uma comunidade de destino livre da doença. Métodos. Usando um modelo SEIRV-SEI para humanos e vetores, foram aplicadas simulações numéricas aos seguintes cenários: (1) migração de uma comunidade endêmica para uma comunidade de destino livre da doença, comparando o desempenho de Haemagogus janthinomys e de Aedes aegypti como vetores; (2) migração através de uma comunidade de trânsito localizada em uma rota migratória, onde a doença é endêmica, para uma comunidade de destino livre da doença; e (3) efeitos de diferentes taxas de vacinação na comunidade de destino, considerando-se a vacinação dos migrantes ao chegarem. Resultados. Os resultados não revelaram diferenças marcantes entre os cenários 1 e 2. O tipo de vetor e a cobertura vacinal na comunidade de destino são mais relevantes para a ocorrência de surtos do que as taxas de migração; o vetor H. janthinomys é mais efetivo do que A. aegypti. Conclusões. Na medida em que a vacinação é mais determinante para um potencial surto que as taxas de migração, a vacinação de migrantes na chegada pode ser uma das medidas mais efetivas contra a febre amarela. Além disso, o H. janthinomys é um vetor mais competente do que o A. aegypti em densidades similares, mas a presença de A. aegypti é um alerta para manter a vacinação acima dos níveis recomendados.
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ABSTRACT BACKGROUND: After validation in multiple types of liver disease patients, the MELD score was adopted as a standard by which liver transplant candidates with end-stage liver disease were prioritized for organ allocation in the United States since 2002, and in Brazil, since 2006. AIMS: To analyze the mortality profile of patients on the liver transplant waiting list correlated to MELD score at the moment of transplantation. METHODS: This study used the data from the Secretary of Health of the São Paulo State, Brazil, which listed 22,522 patients, from 2006 (when MELD score was introduced in Brazil) until June 2009. Patients with acute hepatic failure and tumors were included as well. We also considered the mortality of both non-transplanted and transplanted patients as a function of the MELD score at presentation. RESULTS: Our model showed that the best MELD score for patients on the liver transplant waiting list associated to better results after liver transplantation was 26. CONCLUSIONS: We found that the best score for applying to liver transplant waiting list in the State of São Paulo was 26. This is the score that minimizes the mortality in both non-transplanted and liver transplanted patients.
RESUMO RACIONAL: Desde 2002, após validação em múltiplos tipos de hepatopatias, o escore MELD foi adotado como padrão pelo qual os candidatos a transplante de fígado com doença hepática terminal têm sido priorizados para alocação de órgãos nos Estados Unidos, e em 2006 no Brasil. OBJETIVOS: Analisar a mortalidade de pacientes em lista de espera para transplante de fígado correlacionando com o MELD, no momento do transplante. MÉTODOS: Foram utilizados os dados da Secretaria de Saúde do Estado de São Paulo, Brasil, onde foram listados 22.522 pacientes, desde 2006 (quando o escore MELD foi introduzido no Brasil) até junho de 2009. Foram incluídos pacientes com falência hepática e tumores. A mortalidade de pacientes não transplantados e transplantados também foi considerada em função do escore MELD. RESULTADOS: Nosso modelo mostrou que o melhor valor do MELD, em pacientes em lista de espera para transplante e com melhores resultados, foi de 26. Este valor minimiza mortalidade em pacientes não transplantados bem comem pacientes na lista de espera para transplante de fígado. CONCLUSÕES: O escore MELD ótimo para entrar na lista de espera para transplante de fígado, no estado de São Paulo, é em torno de 26. Esse é o valor que minimiza a mortalidade tanto dos pacientes não transplantados em lista de espera, quanto dos submetidos à transplante de fígado.