SARIMA for predicting the cases numbers of dengue SARIMA para predição do número de casos de dengue

Introduction: Forecasting dengue cases in a population by using time-series models can provide useful information that can be used to facilitate the planning of public health interventions. The objective of this article was to develop a forecasting model for dengue incidence in Campinas, southeast Brazil, considering the Box-Jenkins modeling approach. Methods: The forecasting model for dengue incidence was performed with R software using the seasonal autoregressive integrated moving average (SARIMA) model. We fitted a model based on the reported monthly incidence of dengue from 1998 to 2008, and we validated the model using the data collected between January and December of 2009. Results: SARIMA (2,1,2) (1,1,1)12 was the model with the best fit for data. This model indicated that the number of dengue cases in a given month can be estimated by the number of dengue cases occurring one, two and twelve months prior. The predicted values for 2009 are relatively close to the observed values. Conclusions: The results of this article indicate that SARIMA models are useful tools for monitoring dengue incidence. We also observe that the SARIMA model is capable of representing with relative precision the number of cases in a next year.


Response to letter to the editor: simple statistical models can provide good predictions of dengue incidence
Resposta à carta ao editor: modelos estatísticos simples podem trazer boas predições da incidência da dengue Edson Zangiacomi Martinez 1 , Amaury Lelis Dal Fabbro 1 and Elisângela Aparecida Soares da Silva 1

Dear Editor,
We thank Professor Wiwanitkit for his interest in our research on forecast models for dengue incidence 1,2 .We are glad for the opportunity to clarify some important points of our research.
First, Professor Wiwanitkit has argued that two articles produced by our research group might be a salami publication.Salami-slicing denotes a type of research misconduct that consists of dividing the results of a research project into a series of articles to maximize the number of publications 3,4 , and we strongly disagree that our articles 1,2 are an example of this bad practice.Each of these articles tells its own story, although they present a discussion of the use of the same data analysis strategy.Further, each article deals with different data sets obtained from two different municipalities, evidencing that these localities have different temporal patterns of dengue incidence, and summarizing all these results into a single article would result in a great loss of information and details.
Second, he has stated that the prediction is based on the retrospective data, which might not be useful for future prediction in actual life due to the current rapid change in environmental factors.However, we believe that the high volatility observed in some periods of the time series are primarily due to the introduction and reintroduction of different virus serotypes in a susceptible population, and the results of our articles suggest that the model fits the data adequately, despite the occurrence of this phenomenon within the studied period 1,2 .In addition, the out-of-sample predictions generated by the SARIMA models are close to the observed values, suggesting that the model is useful and accurate for forecasting purposes.

INTRODUCTION
Dengue is a disease of great importance for public health in tropical and sub-tropical areas of the world.The disease is transmitted by the bites of infected Aedes mosquitoes, and its symptoms, which include headache and muscle and joint pain, are very similar to those of fever-causing illnesses.It is estimated that between 50 and 100 million cases of dengue fever occur each year1,2, and about two-thirds of the world's population live in areas infested with dengue vectors3.In the first decade of the 21st century, Brazil ranked among the countries with the highest dengue incidence in the world4.In Brazil, more than three million cases were reported from 2000 to 2005, comprising approximately 70% of reported dengue fever cases in the Americas5.
Dengue can be caused by any of the four serotypes of dengue virus, designated DEN-1, DEN-2, DEN-3, and DEN-4.In Brazil, the first laboratory-confirmed dengue outbreak was reported in 1981-1982 in the State of Roraima6, and no further dengue activity was reported until 1986 with the introduction of DEN-1 in the State of Rio de Janeiro7.The DEN-2 serotype was introduced in 1990 in Rio de Janeiro during a period of DEN-1 serotype circulation8.In the following years, the DEN-2 serotype spread to other Brazilian regions, with more severe clinical presentations9.In 1994, DEN-3 virus was reintroduced in the Americas after an absence of 16 years, and in 2000, it was introduced in Rio de Janeiro, causing a large epidemic of dengue fever10,11.The first report of DEN-4 in Brazil was in the State of Roraima in 198212.
Mathematical and statistical models can provide substantial contributions to the understanding of the dynamics of dengue transmission and the trends of growth in the number of cases of the disease.Recently, statistical tools such as time series analyses13,14 have been used by several authors to describe and forecast the number of cases of dengue in specific populations15-19.Among these models, the seasonal autoregressive integrated moving average http://dx.doi.org/10.1590/S0037-86822011000400007