Surto epidêmico de sarampo na Ilha Grande, Rio de Janeiro, Brasil

Abstract

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Stochastic Modeling of a Measles Outbreak in Brazil

“…Through numerical simulations implemented in Python, we compute all the specific properties of stochastic modeling and it was possible to estimate a rate of spread for the epidemic outbreak in Ilha Grande. All the computed values through SIR CTMC model for this specific measles outbreak, were in good agreement with the reported results [3], showing a better behaviour than the deterministic SIR model. From the simulation, it was possible to estimate a rate of spread for the epidemic outbreak, in good agreement with the expected value for measles disease.…”

“…The parameters values used for performing numerical simulations were taken from a report on an epidemic measles outbreak in a fishing village in the Ilha Grande region, in the state of Rio de Janeiro, Brazil, in 1976 [3]. The total population of residents in the village was 453 individuals.…”

“…In the analysis of a measles outbreak, there are some age groups that do not get infected. It is the situation for individuals over 19 years, who have been previously vaccinated or are considered to have natural immunity, given that a measles outbreak have occurred five years earlier, and also for children under 1 year, who are supposed to have maternal immunity [3]. Consequently, population group aged between 1 and 19 years was defined as the susceptible population, comprising 220 individuals.…”

“…With no previous information on R 0 or the contagion and recovering rates, these parameters can be computed through several analytical or numerical techniques, including least square principle [7], Next Generation Matrix, graph theory and others (see reference [4] and references therein). In this study, it is used the basic reproduction number R 0 = 6.92 as it was defined in the reported case study, reference [3].…”

“…In this work, we consider two stochastic versions of the SIR model for analysing a measles outbreak in Ilha Grande, Rio de Janeiro, in 1976 [3]. We use a Continuous Time Markov Chain [2], which allows a detailed follow-up of the epidemic dynamics.…”