Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil

Abstract

OBJECTIVE:To estimate the basic reproduction number (R 0 ) of dengue fever including both imported and autochthonous cases. METHODS:The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fi tting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R 0 of imported versus autochthonous cases was used as an estimator of real R 0 . RESULTS:The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R 0 above one, although the real R 0 was below one. The same results were seen when the method was applied on simulated epidemics with fi xed R 0 . This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R 0 values. CONCLUSIONS:It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease. The quick expansion of vectors and viruses throughout nearly all Brazilian states is facilitated by ever increasing moving and traveling of people in the country. Until recent years in most localities the origin of dengue cases was neither reported nor investigated. To the authors' best knowledge, no study has been published investigating the impact of "imported" cases on the dynamics of the epidemics. The origin of each case in the 2002-2003 epidemics in Brasília was inferred after a detailed survey of the patient's background, taking into account the duration of the incubation phase of the disease. As these data about the most probable origin of these cases were available, we investigated its possible impact on the dynamics of dengue epidemics. We compared its dynamics with the outputs of a simple "susceptibleinfectious-resistant" (SIR) model modifi ed in order to include the input of daily numbers of imported cases when estimating the basic reproduction number (R 0 ). DESCRIPTORS:Mathematical modeling is a powerful tool to simulate real past situations, to input data from the present and hopefully to forecast future outcomes.6 It has been widely used to understand the dynamics of infectious RESUMO OBJETIVO: Estimar o número básico de reprodução da dengue (R 0 ), com base nos casos importados, além dos casos autóctones. MÉTODOS:O estudo foi feito sobre dados epidemiológicos da epidemia de dengue em Brasília, 2003. O número básico de reprodução é determinado a partir da curva epidêmica, ajustando uma reta ao crescimento inicial do número de casos. Para simular uma epidemia com casos autóctones e importados, foi criado um modelo compartimentado do tipo "suscetíveis-infectadosr...

Epidemiology, management, complications and costs associated with type 2 diabetes in Brazil: a comprehensive literature review

“…The Brazilian longitudinal study of adult health (ELSA-Brasil) [69,70] is a multicentre cohort study funded by the Ministry of Health to investigate diabetes and cardiovascular disease (CVD) incidence, risk factors and complications. The baseline evaluation was completed in December 2010 and included 15,105 civil servants aged 35–74 years from six public universities in the northeast, south and southeast regions of Brazil.…”

“…The baseline evaluation was completed in December 2010 and included 15,105 civil servants aged 35–74 years from six public universities in the northeast, south and southeast regions of Brazil. Annual telephone interviews are conducted to monitor the health status of each participant enrolled in the baseline [69]. …”

Estimation of reproduction number and probable vector density of the first autochthonous dengue outbreak in Japan in the last 70 years

“…The initial growth in the number of cases is considered to be exponential with parameter k. The estimated reproduction number R 0i at the start of the epidemic is calculated by the following equation, modified from the method of Massad et al [5,6].…”

“…The number of female mosquitoes per person (MPP) has been used as vector density, and the reproduction number R 0 is directly proportional to the MPP under the assumption that the biting rate of the vector is steady in the following equation [6,8].…”

“…where m is the MPP, a is the daily biting rate of the mosquitoes, and b and c are the probabilities of viral transmission from an infected mosquito to a susceptible human, and from an infected human to mosquito, respectively [6]. Parameters l, c, and s e are used as in Eq.…”