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- Instituto Oswaldo Cruz, Ministério da Saúde
- ELSEVIER SCIENCE BV
- ELSEVIER SCIENCE BV; AMSTERDAM
- Springer; Nova York
- Biblioteca Digital da Unicamp
- Taylor and Francis
- Universidade do Minho
- Hindawi Publishing Corporation
- Elsevier
- Taylor & Francis
- Public Library of Science
- Fundação Calouste Gulbenkian
- FUNDACO OSWALDO CRUZ; RIO DE JANEIRO, RJ
- Universidade Cornell
- Instituto Nacional de Salud Pública
- Mais Publicadores...

## Dynamics of the 2006/2007 dengue outbreak in Brazil

Fonte: Instituto Oswaldo Cruz, Ministério da Saúde
Publicador: Instituto Oswaldo Cruz, Ministério da Saúde

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

65.89%

We analyzed dengue incidence in the period between October 2006-July 2007 of 146 cities around the country were Larval Index Rapid Assay (LIRA) surveillance was carried out in October 2006. Of these, we chosen 61 cities that had 500 or more cases reported during this period. We calculated the incidence coefficient, the force of infection (») and the basic reproduction number (R0) of dengue in those 61 cities and correlated those variables with the LIRA. We concluded that » and R0 are more associated with the number of cases than LIRA. In addition, the average R0 for the 2006/2007 dengue season was almost as high as that calculated for the 2001/2002 season, the worst in Brazilian history.; CNPq; FAPESP; FMUSP - HC

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## On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Fonte: ELSEVIER SCIENCE BV
Publicador: ELSEVIER SCIENCE BV

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

95.99%

#Basic reproduction number#Epidemiology#Ordinary differential equations#Probabilistic cellular automata#Random networks#SIR model#VACCINATION STRATEGY#MOUTH-DISEASE#MODEL#DYNAMICS#TRANSMISSION

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.; CNPq

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## On estimating the basic reproduction number in distinct stages of a contagious disease spreading

Fonte: ELSEVIER SCIENCE BV; AMSTERDAM
Publicador: ELSEVIER SCIENCE BV; AMSTERDAM

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

96.02%

#BASIC REPRODUCTION NUMBER#COMPLEX NETWORK#EPIDEMIOLOGY#ORDINARY DIFFERENTIAL EQUATIONS#PROBABILISTIC CELLULAR AUTOMATA#CELLULAR-AUTOMATA#INFECTIOUS-DISEASES#EPIDEMIOLOGIC MODELS#AIRBORNE INFECTIONS#CONTACT NETWORK#R-0

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA)...

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## A comparative analysis of the relative efficacy of vector-control strategies against dengue fever

Fonte: Springer; Nova York
Publicador: Springer; Nova York

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

66.02%

#Dengue#Basic reproduction number#Force of infection#Sensitivity analysis#Vector control#DOENÇAS TRANSMISSÍVEIS#MODELOS MATEMÁTICOS#FEBRE HEMORRÁGICA DA DENGUE

Dengue is considered one of the most important vector-borne infection, affecting almost half of the world population with 50 to 100 million cases every year. In this paper, we present one of the simplest models that can encapsulate all the important variables related to vector control of dengue fever. The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neglecting seasonal variation, we calculate the equilibrium values of the model’s variables. We also present a sensitivity analysis of the impact of four vector-control strategies on the Basic Reproduction Number, on the Force of Infection and on the human prevalence of dengue. Each of the strategies was studied separately from the others. The analysis presented allows us to conclude that of the available vector control strategies...

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## Estimação do número de reprodução basal em modelos compartimentais; Estimation of the basic reproduction number in compartimental models

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 24/02/2014
PT

Relevância na Pesquisa

66.07%

#Modelos compartimentais (Matemática)#Epidemiologia - Modelos matemáticos#Epidemiologia - Métodos estatísticos#Biomatemática#Compartimental models (Mathematics)#Epidemiology#Epidemiology#Biomathematics

Uma das quantidades mais importante definida na epidemiologia é o número de reprodução basal, ou básico, associado com a pandemia e denotado por $R_0$. Ele proporciona uma medida da intensidade das intervenções necessárias para o controle da epidemia. Ao mesmo tempo, os modelos epidemiológicos compartimentais SIR, SEIR, tanto no enfoque enfoque determinístico quanto no estocástico, têm sido de grande ajuda para a compreensão dos mecanismos de transmissão de doenças infecciosas em todo o mundo. Esta dissertação apresenta alguns métodos para estimar esta quantidade através da utilização dos modelos epidemiológicos compartimentais. São considerados os quatro métodos apresentados por Chowell et al. (Mathematical Biosciences, 2007, v. 208, p. 571-589). O primeiro método é baseado na taxa de crescimento (inicial) exponencial da epidemia. Dada a taxa de crescimento exponencial e o modelo subjacente temos uma estimativa de $R_{0}$. No caso dos métodos 2 e 3 o processo de estimação do $R_0$ baseia-se nos modelos compartimentais, modelos SIR e SEIR no método 2, e em um modelo SEIR estendido no método 3. O método 4 utiliza uma abordagem bayesiana do modelo SIR estocástico. O objetivo da dissertação é estudar as propriedades dos estimadores baseados nos métodos 1...

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## Dengue disease, basic reproduction number and control

Fonte: Taylor and Francis
Publicador: Taylor and Francis

Tipo: Artigo de Revista Científica

Publicado em //2012
ENG

Relevância na Pesquisa

96.07%

Dengue is one of the major international public health concerns.Although progress is underway, developing
a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control.
A model for the transmission of dengue disease is presented. It consists of eight mutually exclusive compartments
representing the human and vector dynamics. It also includes a control parameter (insecticide) in
order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE)
and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever
a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show
that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number
below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.; Fundação para a Ciência e a Tecnologia (FCT)

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## Control of dengue disease : a case study in Cape Verde

Fonte: Universidade do Minho
Publicador: Universidade do Minho

Tipo: Conferência ou Objeto de Conferência

Publicado em //2010
ENG

Relevância na Pesquisa

65.99%

Preprint. The published version is:
Proceedings of the 10th International Conference
on Computational and Mathematical Methods
in Science and Engineering (CMMSE 2010),
Almería (Andalucía), Spain, June 26-30 2010, 816–822.; A model for the transmission of dengue disease is presented. It consists of eight
mutually-exclusive compartments representing the human and vector dynamics.
It also includes a control parameter (adulticide spray) in order to combat the
mosquito. The model presents three possible equilibria: two disease-free equilibria
(DFE) — where humans, with or without mosquitoes, live without the disease
— and another endemic equilibrium (EE). In the literature it has been proved
that a DFE is locally asymptotically stable, whenever a certain epidemiological
threshold, known as the basic reproduction number, is less than one. We show that
if a minimum level of insecticide is applied, then it is possible to maintain the basic
reproduction number below unity. A case study, using data of the outbreak that
occured in 2009 in Cape Verde, is presented.; Fundação para a Ciência e a Tecnologia (FCT)

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## Sensitivity analysis in a dengue epidemiological model

Fonte: Hindawi Publishing Corporation
Publicador: Hindawi Publishing Corporation

Tipo: Conferência ou Objeto de Conferência

Publicado em //2013
ENG

Relevância na Pesquisa

65.91%

Epidemiological models may give some basic guidelines for public health practitioners, allowing the analysis of issues that can
influence the strategies to prevent and fight a disease. To be used in decision making, however, a mathematical model must be
carefully parameterized and validated with epidemiological and entomological data. Here an SIR (S for susceptible, I for infectious,
and R for recovered individuals) and ASI (A for the aquatic phase of themosquito, S for susceptible, and I for infectiousmosquitoes)
epidemiological model describing a dengue disease is presented, as well as the associated basic reproduction number. A sensitivity
analysis of the epidemiological model is performed in order to determine the relative importance of the model parameters to the
disease transmission.

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## Optimal control for a tuberculosis model with reinfection and post-exposure interventions

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

65.89%

#Epidemic model#Optimal control theory#Treatment strategies#Tuberculosis#Basic reproduction number#Epidemic models#Optimal control strategy#System of ordinary differential equations#Transmission coefficients#Control theory#Ordinary differential equations

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure interventions. They depend on the parameters of the model and reduce effectively the number of active infectious and persistent latent individuals. The time that the optimal controls are at the upper bound increase with the transmission coefficient. A general explicit expression for the basic reproduction number is obtained and its sensitivity with respect to the model parameters is discussed. Numerical results show the usefulness of the optimization strategies. © 2013 Elsevier Inc.

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## Dengue disease, basic reproduction number and control

Fonte: Taylor & Francis
Publicador: Taylor & Francis

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

96.07%

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented. Copyright © 2012 Taylor and Francis Group, LLC.

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## Dynamics of the 2006/2007 dengue outbreak in Brazil

Fonte: Instituto Oswaldo Cruz, Ministério da Saúde
Publicador: Instituto Oswaldo Cruz, Ministério da Saúde

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/09/2008
EN

Relevância na Pesquisa

65.89%

We analyzed dengue incidence in the period between October 2006-July 2007 of 146 cities around the country were Larval Index Rapid Assay (LIRA) surveillance was carried out in October 2006. Of these, we chosen 61 cities that had 500 or more cases reported during this period. We calculated the incidence coefficient, the force of infection (») and the basic reproduction number (R0) of dengue in those 61 cities and correlated those variables with the LIRA. We concluded that » and R0 are more associated with the number of cases than LIRA. In addition, the average R0 for the 2006/2007 dengue season was almost as high as that calculated for the 2001/2002 season, the worst in Brazilian history.

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## The Basic Reproduction Number as a Predictor for Epidemic Outbreaks in Temporal Networks

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

Publicado em 20/03/2015
EN

Relevância na Pesquisa

65.89%

The basic reproduction number R0—the number of individuals directly infected by an infectious person in an otherwise susceptible population—is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction of people infected once the outbreak is over, Ω. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R0 and Ω. However, if one considers disease spreading on a temporal contact network—where one knows when contacts happen, not only between whom—then larger R0 does not necessarily imply larger Ω. In this paper, we numerically investigate the relationship between R0 and Ω for a set of empirical temporal networks of human contacts. Among 31 explanatory descriptors of temporal network structure, we identify those that make R0 an imperfect predictor of Ω. We find that descriptors related to both temporal and topological aspects affect the relationship between R0 and Ω, but in different ways.

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## Early real-time estimation of the basic reproduction number of emerging or reemerging infectious diseases in a community with heterogeneous contact pattern: Using data from Hong Kong 2009 H1N1 Pandemic Influenza as an illustrative example

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

Publicado em 15/09/2015
EN

Relevância na Pesquisa

66.02%

Emerging and re-emerging infections such as SARS (2003) and pandemic H1N1 (2009) have caused concern for public health researchers and policy makers due to the increased burden of these diseases on health care systems. This concern has prompted the use of mathematical models to evaluate strategies to control disease spread, making these models invaluable tools to identify optimal intervention strategies. A particularly important quantity in infectious disease epidemiology is the basic reproduction number, R0. Estimation of this quantity is crucial for effective control responses in the early phase of an epidemic. In our previous study, an approach for estimating the basic reproduction number in real time was developed. This approach uses case notification data and the structure of potential transmission contacts to accurately estimate R0 from the limited amount of information available at the early stage of an outbreak. Based on this approach, we extend the existing methodology; the most recent method features intra- and inter-age groups contact heterogeneity. Given the number of newly reported cases at the early stage of the outbreak, with parsimony assumptions on removal distribution and infectivity profile of the diseases, experiments to estimate real time R0 under different levels of intra- and inter-group contact heterogeneity using two age groups are presented. We show that the new method converges more quickly to the actual value of R0 than the previous one...

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## On the Final Size of Epidemics with Seasonality

Fonte: Fundação Calouste Gulbenkian
Publicador: Fundação Calouste Gulbenkian

Tipo: Artigo de Revista Científica

Publicado em //2009
ENG

Relevância na Pesquisa

65.99%

We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary, the basic reproduction number ℛ0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.

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## Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

Fonte: FUNDACO OSWALDO CRUZ; RIO DE JANEIRO, RJ
Publicador: FUNDACO OSWALDO CRUZ; RIO DE JANEIRO, RJ

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

75.91%

#VECTOR-BORNE INFECTIONS#BASIC REPRODUCTION RATE#SPOROZOITE RATE#VECTORIAL CAPACITY#FORCE OF INFECTION#DIMENSIONAL ANALYSIS#TRANSMISSION#R-0#PARASITOLOGY#TROPICAL MEDICINE

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' threshold theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.; European Union [282589]; European Union; LIM01 HCFMUSP; LIM01 HCFMUSP; CNPq; CNPq

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## Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

Fonte: Instituto Oswaldo Cruz, Ministério da Saúde
Publicador: Instituto Oswaldo Cruz, Ministério da Saúde

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/06/2012
EN

Relevância na Pesquisa

75.91%

#vector-borne infections#basic reproduction rate#sporozoite rate#vectorial capacity#force of infection#dimensional analysis

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

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## Dengue disease, basic reproduction number and control

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/03/2011

Relevância na Pesquisa

65.99%

#Mathematics - Optimization and Control#Computer Science - Systems and Control#Physics - Medical Physics#Quantitative Biology - Other Quantitative Biology#92B05, 93C95, 93D20

Dengue is one of the major international public health concerns. Although
progress is underway, developing a vaccine against the disease is challenging.
Thus, the main approach to fight the disease is vector control. A model for the
transmission of Dengue disease is presented. It consists of eight mutually
exclusive compartments representing the human and vector dynamics. It also
includes a control parameter (insecticide) in order to fight the mosquito. The
model presents three possible equilibria: two disease-free equilibria (DFE) and
another endemic equilibrium. It has been proved that a DFE is locally
asymptotically stable, whenever a certain epidemiological threshold, known as
the basic reproduction number, is less than one. We show that if we apply a
minimum level of insecticide, it is possible to maintain the basic reproduction
number below unity. A case study, using data of the outbreak that occurred in
2009 in Cape Verde, is presented.; Comment: This is a preprint of a paper whose final and definitive form has
appeared in International Journal of Computer Mathematics (2011), DOI:
10.1080/00207160.2011.554540

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## The basic reproduction number as a predictor for epidemic outbreaks in temporal networks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/07/2014

Relevância na Pesquisa

65.89%

#Quantitative Biology - Populations and Evolution#Computer Science - Social and Information Networks#Physics - Physics and Society

The basic reproduction number R0 -- the number of individuals directly
infected by an infectious person in an otherwise susceptible population -- is
arguably the most widely used estimator of how severe an epidemic outbreak can
be. This severity can be more directly measured as the fraction people infected
once the outbreak is over, {\Omega}. In traditional mathematical epidemiology
and common formulations of static network epidemiology, there is a
deterministic relationship between R0 and {\Omega}. However, if one considers
disease spreading on a temporal contact network -- where one knows when
contacts happen, not only between whom -- then larger R0 does not necessarily
imply larger {\Omega}. In this paper, we numerically investigate the
relationship between R0 and {\Omega} for a set of empirical temporal networks
of human contacts. Among 31 explanatory descriptors of temporal network
structure, we identify those that make R0 an imperfect predictor of {\Omega}.
We find that descriptors related to both temporal and topological aspects
affect the relationship between R0 and {\Omega}, but in different ways.

Link permanente para citações:

## A model for the A(H1N1) epidemic in Mexico, including social isolation

Fonte: Instituto Nacional de Salud Pública
Publicador: Instituto Nacional de Salud Pública

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/02/2011
EN

Relevância na Pesquisa

65.95%

OBJECTIVE: We present a model for the 2009 influenza epidemic in Mexico to describe the observed pattern of the epidemic from March through the end of August (before the onset of the expected winter epidemic) in terms of the reproduction number and social isolation measures. MATERIAL AND METHODS: The model uses a system of ordinary differential equations. Computer simulations are performed to optimize trajectories as a function of parameters. RESULTS: We report on the theoretical consequences of social isolation using published estimates of the basic reproduction number. The comparison with actual data provides a reasonable good fit. CONCLUSIONS: The pattern of the epidemic outbreak in Mexico is characterized by two peaks resulting from the application of very drastic social isolation measures and other prophylactic measures that lasted for about two weeks. Our model is capable of reproducing the observed pattern.

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## A model for the A(H1N1) epidemic in Mexico, including social isolation

Fonte: Instituto Nacional de Salud Pública
Publicador: Instituto Nacional de Salud Pública

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/02/2011
EN

Relevância na Pesquisa

65.95%

OBJECTIVE: We present a model for the 2009 influenza epidemic in Mexico to describe the observed pattern of the epidemic from March through the end of August (before the onset of the expected winter epidemic) in terms of the reproduction number and social isolation measures. MATERIAL AND METHODS: The model uses a system of ordinary differential equations. Computer simulations are performed to optimize trajectories as a function of parameters. RESULTS: We report on the theoretical consequences of social isolation using published estimates of the basic reproduction number. The comparison with actual data provides a reasonable good fit. CONCLUSIONS: The pattern of the epidemic outbreak in Mexico is characterized by two peaks resulting from the application of very drastic social isolation measures and other prophylactic measures that lasted for about two weeks. Our model is capable of reproducing the observed pattern.

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