DENGUE OUTBREAK EARLY IDENTIFICATION BY RAIN AND HUMAN CASES EVOLUTION IN FORTALEZA/CE

ABSTRACT

This article presents an analytical evaluation of the behavior of dengue in the city of Fortaleza/CE, throughout all the epidemiological weeks of years 2007 to 2021, considering only the influence of rainfall on the increase of dengue in the municipality. The high correlation between the two events is shown through graphs of the global percentages over time and cross correlation, which imply the emergence of dengue outbreaks from the 13^th epidemiological week for two consecutive years (2012 and 2013), taken as an example of investigation. In addition, the study shows that the amounts of rain falling between the 5^th and 9^th epidemiological weeks indicate the beginning of dengue outbreaks with greater or lesser intensity. We confirm cross correlation using Ljung-Box and Shapiro-Wilk statistical tests between rain and dengue SARIMA curves we found for the period, meaning that the rain explains Dengue human cases up to four weeks before they happen, applying SARIMA models to both events. Finally, we also show, by using instantaneous increase measures along epidemiological accumulated weeks from years 2007-2019, the outbreak identification, to better indicate to health managers its presence.

Keywords:
analytical prediction; dengue control; cross correlation

1 INTRODUCTION

Dengue fever outbreaks are some of the greatest public health issues currently affecting many cultures around the world.

Dengue fever outbreaks are some of the greatest public health issues currently affecting many cultures around the world, particularly those in the southern regions of America and Africa. Approximately 50 years have passed since this epidemic began (PAHO/WHO, 2019).

Although dengue vaccines have been researched for decades, neither an effective nor financially viable vaccine exists (GLOBO, 2022; Santos et al., 2021; Ismail et al., 2022). Despite the Butantan Institute’s efforts in this regard, it is not anticipated that research will move from the stage of clinical trials to industrial production until 2024. However, even Butantan researchers claim that the vaccination should not be the main method of dengue prevention (BUTANTAN, 2021).

Consequently, in Brazil, as well as in other countries of the world, actions to combat dengue and other arboviruses primarily conducted by municipal departments of endemic diseases have centered on attempting to interrupt the proliferation cycle of the mosquito vector of these diseases the Aedes Aegypti through preventive actions carried out by endemic disease control agents to eliminate the accumulation of standing water, which favors the mosquito’s life cycle. However, there are aggravating elements that might make this effort more challenging, such as the disorder of urban environments, the absence or precariousness of basic sanitary facilities, and the lack of education and public awareness. Rainfall, especially when it happens in irregular patterns, increases the sources of stagnant water, particularly in urban areas, and has been identified as a natural aggravating factor for the spread of Aedes Aegypti. Understanding the dependence patterns of this last element can lead to a more effective effort to combat the Aedes Aegypti life cycle.

According to the World Health Organization (WHO) (2022), a disease outbreak is the occurrence of an abnormally high number of cases in a single community, geographical area, or region. Infectious agents that spread directly from person to person, from exposure to an animal reservoir or other environmental sources, or through a bug or any animal vector, are responsible for maintaining outbreaks. Human behavior almost always contributes to the spread of disease. Detection and disclosure of such events in a timely manner are essential for mitigating their harmful social and economic effects.

Outbreaks are sudden events, rapidly accompanied by actions of the health care system to save lives and prevent new instances. However, the term “outbreak” is typically employed when diseases emerge in a relatively restricted geographic area. If a disease outbreak spreads swiftly to several individuals greater than specialists anticipate and extends throughout a vast geographical area, it is sometimes referred to as an epidemic.

The main objective of this work is to support the claims of Negreiros et al. (2007) regarding the correlation between the evolution of precipitation and the evolution of dengue cases in Fortaleza/Ce; and to achieve this goal, a semi-automatic outbreak of dengue fever cases identification methodology was developed using R scripts (R Development Core Team, 2023). In the scope of this study, outbreak is defined how the point in time when starts the maximum rate of increase of the curve of dengue number of cases in function of epidemiological weeks; in other words, it is the point (week) of maximum variation on the cumulative distribution function curve of dengue number of cases. This study intends to locate this point using R scripts for data analysis. Operating over cumulative percentage cases of dengue curve, R algorithms iteratively calculates accumulated difference from a determinate fixed number of weeks ahead to the week in analysis. The fixed periods explored in this study were 2, 4 and 6 weeks. The point from which the maximum difference could be calculated is defined to be the outbreak point.

The difficulty of recognizing “outbreaks” in endemic diseases entails locating the moment that favors the disease’s exponential growth in a particular population within a certain geographic region. The automatic detection of “outbreaks” has been researched as a means of predicting incidents that pose a serious threat to the community. In general, detections result from a variety of elements that lead to the identification of an abnormal behavior that is responsible for the sudden spread of a disease. The study of elements or events highly correlated in cause-and-effect can lead to an anticipation of a disease outbreak problem. Caused by the presence of the Aedes Aegypti mosquito, the growth of Dengue fever is related to climatic factors such as the incidence of precipitation (increased humidity and/or temperature).These factors have been found to play a significant role in triggering the development of the disease. But how exactly does this occur? Initially, each location in the world’s tropics has its own tale, as may be seen in the examples below. Table 1 lists the main articles (divided, for convenience, in outside Brazil and Brazilian studies) that currently investigate the relationships between dengue, rain, and cross correlation function, defining those that will be explored in greater detail in this work. In Table 1, Title indicates the title of the paper, Brief indicates the summary of the results, Country indicates the country where the research was applied, Reference indicates the authors and Selected indicates if we use it or not for our evaluations.

Table 1
Main related articles.

Title	Brief	Country	Reference	Selected?
Optimal Lead Time for Dengue Forecast	Prediction of a rise in dengue cases and sufficient time to allow timely decisions	Singapore	Hii, Y. L. et al. (2012)	No
Climate and Dengue Fever: Early warning based on temperature and rainfall	Forecast of dengue cases based on temperature and cumulative rainfall	Singapore	Hii, Y. L. (2013)	No
Impact of meteorological factors on the spatiotemporal patterns of dengue fever incidence	This study presents a novel integration of a distributed lag nonlinear model and Markov random fields to assess the nonlinear lagged effects of weather variables on temporal dynamics of dengue fever and to account for the geographical heterogeneity	Taiwan	Chien, L-C.; Yu, H-L. (2014)	Yes
Data mining techniques for predicting dengue outbreak in geospatial domain using weather parameters for New Delhi, India	Forecast of dengue cases based on data mining techniques, like as multi-regression and Naive-Bayes approach to model the relation between dengue cases and weather parameters.	India	Agarwal, N. et al. (2018)	No
Ensemble method for dengue prediction	Forecast of dengue cases using ensemble models created by combining three disparate types of component models: two-dimensional Method of Analogues models incorporating both dengue and climate data; additive seasonal Holt-Winters models with and without wavelet smoothing; and simple historical models.	Peru and Puerto Rico	Buczak, A. L. et al. (2018)	Yes
Revisiting the role of rainfall variability and its interactive effects with the built environment in urban dengue outbreaks.	This study identifies the meteorological measurements most relevant to dengue variations, namely weekly minimum temperature, and weekly maximum 24-hour precipitation, obtaining the relative risk (RR) in relation to the number of human cases and a continuous lag period of 20 weeks.	Taiwan	Chen, T-H. K.; Chen, V. Y-J.; Wen, T. (2018)	Yes
A combination of climatic conditions determines major within-season dengue outbreaks in Guangdong Province, China	Forecast of dengue cases based on multi-scale modeling framework, parameterized by available weather, vector and human case data.	China	Wang X, et al. (2019)	No
Prediction of dengue outbreaks in Kerala state using disease surveillance and meteorological data	Forecast of dengue cases based on multivariate (temperature and cumulative rainfall) models.	India	Nayak, S. D. P.; Narayan, K. A. (2020)	Yes
An Association between Rainy Days with Clinical Dengue Fever in Dhaka, Bangladesh: Findings from a Hospital Based Study	Identification of the influence of climatic variability on the occurrence of clinical dengue requiring hospitalization	Bangladesh	Rahman, K. M. et al. (2020)	No
An accurate mathematical model predicting number of dengue cases in tropics.	Forecast of dengue cases using model based on machine learning technique and multivariate approach.	Sri Lanka	Edussuriya, C.; Deegalla, S.; Gawarammana, I. (2021)	Yes
Dengue disease dynamics are modulated by the combined influences of precipitation and landscape: A machine learning approach	Forecast of dengue cases using a model-based (MOB) recursive partitioning, implemented to test the combined influences of landscape and climate factors on ovitrap index (vector mosquito occurrence) and dengue incidence.	Philippines	Micanaldo, E. F. et al. (2021)	Yes
Predicting the number of dengue cases 8 weeks after	Forecast of dengue cases based on daily temperature and daily rainfall	Singapore	Ying, C. X. et al. (2021)	No
Modeling present and future climate risk of dengue outbreak, a case study in New Caledonia	Forecast of dengue cases based on statistical estimation and a machine learning classifier to estimate the probability for a week to be epidemic under current climate data and this probability was then estimated under climate change scenarios	New Caledonia	Ochida, N. et al. (2022)	No
Prediction of dengue fever outbreaks using climate variability and Markov chain Monte Carlo techniques in a stochastic susceptible-infected-removed model	Forecast of dengue cases based on climate, geography, and environmental factors	Singapore	Martheswaran, T. K. et al. (2022)	No
The practicality of Malaysia dengue outbreak forecasting model as an early warning system	Forecast of dengue cases using and comparing following forecasting models: Autoregressive Distributed Lag (ADL), Hierarchical Forecasting (Bottom-up and Optimal combination) and three Machine Learning methods: (Artificial Neural Network (ANN), Support Vector Machine (SVM) and Random Forest)	Malaysia	Ismail, S. et al. (2022)	Yes
Análise espacial da distribuição dos casos de dengue e a relação com fatores entomológicos, ambientais e socioeconômicos.	This study confirms the characteristic of opportunist species that was already registered for the Aedes aegypti, especially in relation to its ability to quickly adapt to take advantage of different types of containers in the most varied stages of its life.	Brazil	Scandar, S. A. S. (2007)	Yes
Modelo Econométrico para Previsão da Incidência de Dengue no Município do Rio de Janeiro.	Forecast of dengue cases based on an econometric model estimated from time series of dengue cases and climate variables.	Brazil	Amaral, M. R. S.; Vaughon, A. P.; Duarte, K. S. (2009)	Yes
Interação entre fatores socioeconômicos ambientais e ocorrência de casos da dengue no Ceará	Analyze through regression models the impact of environmental socioeconomic variables on notification of dengue cases.	Brazil	Sousa, W. L. et al. (2016)	Yes
Analysis of climate factors and dengue incidence in the metropolitan region of Rio de Janeiro, Brazil	This study examined the incidence of dengue fever related to the climate influence by using temperature and rainfall variables to create a mathematical model based on an auto-regressive moving average with exogenous inputs (ARMAX).	Brazil	Xavier L. L. et al. (2021)	Yes
Impact of Climate Change on Human Infectious Diseases: Dengue	It is analyzed the effect of seasonal factors and the relationship between climate variables and dengue risk	Brazil	Souza, A.; Abreu, M. C.; Oliveira-Júnior, J. F. (2021)	No
Influência do Clima na Incidência de Doenças Causadas pelo Aedes Aegypti no Município de Manaus/AM, Brasil	Forecast of dengue cases based on an ARIMAX model estimated from time series of dengue cases, maximum temperature and rainfall.	Brazil	Santos, P. S. et al. (2021)	Yes

1.1 Findings outside Brazil

Chien and Yu (2014) find that the relationships between rainfall events and dengue incidence are inconsistent, and few studies have examined the impact of the amplitude and frequency of rainfall events on dengue transmission. This study aimed to distinguish between the long-term and short-term impacts of rainfall variance on dengue. The authors intended to examine these impacts in various socioecological contexts in southern Taiwan, a typically epidemic-prone tropical region. This study investigated intraand interannual rainfall variability using a negative binomial multilevel model with Gaussian serial correlation to assess the impact of rainfall on dengue incidence throughout the pre-epidemic and epidemic seasons. Their major findings are that precipitation and dengue incidence have a nonlinear connection in the short-term, with average precipitation throughout the dengue season representing the greatest risk. In addition, rainfall effects were found to interact with household density. The results revealed considerable synergistic relationships between low rainfall frequency and proportion of old dwellings, as well as between cumulative rainfall and proportion of old residences, which contributed to dengue outbreaks. Also, the effects of short-term and long-term rains on ancient structures on the incidence of dengue were differentiated. This means that older neighborhoods may require more public and private attention during rainy periods, to improve environmental quality and promote health in the community.

Chen, T-H. K., Chen, V. Y-J. and Wen (2018) explored recent research linking precipitation and dengue. These authors assessed the health effects of climate change by understanding the connections between climate and dengue. The study examined the delayed non-linear impact of weather on the spatial and temporal fluctuations of dengue fever in southern Taiwan from 1998 to 2011. The study also identified the meteorological measurements most relevant to dengue variations, namely weekly minimum temperature, and weekly maximum 24-hour precipitation, obtaining the relative risk (RR) in relation to the number of human cases and a continuous lag period of 20 weeks. Their findings indicated that the RR increased as the minimum temperature rose, particularly for lag times between 5 and 18 weeks. In addition, they suggested that the time lag for elevated illness risks may be reduced. Once maximum 24-hour precipitation exceeded 50 mm, the corresponding increase in RR persisted for up to 15 weeks. After extreme rainfall, a onemonth drop in dengue RR was observed. In addition, densely inhabited locations were recognized as having a high incidence risk. The results revealed the significant nonlinearity and magnitude of the temporally lagged impacts of temperature and precipitation on dengue outbreaks, which can be used as a practical reference for dengue early warning.

Buczak et al. (2018) employed Machine Learning (“ensemble”) models created by combining three distinct types of components: 1) two-dimensional Analog Method Models incorporating dengue and climate data; 2) additive seasonal Holt-Winters models with and without wavelet smoothing; and 3) simple historical models. Among the individual component models created those with the best performance in the previous four years of data were incorporated into the ensemble models. Separate ensembles were used to predict each of the three targets at each of the two locations. On the findings of peak height and total numbers of dengue cases recorded during a transmission season for the city of Iquitos, Peru, the ensemble models (Machine Learning) scored higher than all other prediction models submitted to the 2015 Dengue Challenge sponsored by five North American agencies. Despite this result, the Machine Learning models provided by the authors did not do well in forecasting the peak week.

Nayak & Narayan (2020) presented analytic investigations employing retrospective secondary data from Kerala state, South India, based on data from the annual integrated disease surveillance reports of dengue cases, rainfall data, and monthly mean temperatures from 2006 to 2017 (144 months). Five distinct dengue case prediction models were built using R software. A model including an optimal combination of climatic variables, and recent and long-term dengue transition was selected as the best fitting among these. Of the 84months forecasts of the training period, 68months forecasts had a negative correlation, 5month forecasts had a positive correlation, 2month forecasts were wrongly negative, and 9month forecasts were incorrectly positive throughout the training period. As a conclusion, they obtained a best predictive generalized additive model that can be developed using the optimal combination of weather predictors and the numbers of dengue cases.

Micanaldo et al. (2021) studied entomological, epidemiological, and vegetation data from the National Epidemiology Center, Department of Health, Manila, Philippines, from 2012 to 2014. Temperature, precipitation, and vegetation data were gathered, by using remote sensing. The authors constructed their model using the R software package “ggpubr”. The model was developed in two stages, with the first (RF) employing a series of machine learning techniques in bagging to construct many bootstrapping trees over small random subsets of data. RF was utilized due to its well-known capacity to manage many predictor variables in the presence of complicated interactions, allowing it to solve a variety of classification and regression issues. This model was used to choose the climatic and vegetation variables. Using the identified key variables, a second model based on recursive partitioning (MOB) was applied to investigate the combined influences of landscape and climate factors on the ovitrap index (Aedes egg traps) and the incidence of dengue. The MOB recursive partitioning for the ovitrap index revealed a high sensitivity of the mosquito vector occurrence in environmental conditions generated by a combination of high residential density areas and low precipitation. In addition, the MOB recursive partitioning revealed a high sensitivity of dengue incidence to precipitation effects in dense residential and commercial areas. The authors concluded that the dynamics of dengue is driven not just by individual climate or landscape impacts, but also by their synergistic or combined effects. This research centered on the identification, through vector surveillance, of regions appropriate for mosquito occurrence under specific climatic conditions, which may be relevant to urban planning techniques for dengue control.

Edussuriya et al. (2021) consider that epidemics are unpredictable and unprecedented. When epidemics develop, health services are overburdened, leading to hospital overcrowding. The authors assert that currently there is no evidence that dengue epidemics can be forecast. Since environmental conditions directly influence the growth of the dengue mosquito, it is plausible that outbreaks might be anticipated using meteorological data. The authors postulated that there is a mathematical relationship between dengue incidence and environmental parameters, and if such a link exists, future dengue cases can be forecasted using recent meteorological data. Also using Machine Learning techniques, a mathematical model was then created. To analyze it, public data for the entire island of Sri Lanka were utilized from the epidemiology unit of the Sri Lankan Ministry of Health, such as the incidence of dengue, average rainfall, humidity, wind speed, temperature, and population density for each district. They discovered that the model could predict the dengue incidence in a particular month in a specific district with accuracy of the root mean square value RMSE between 18 and 35.3. Additionally, using weather data for a given month, the number of dengue cases in subsequent months may be predicted with an RMSE accuracy between 10.4 and 30, with only six of the 19 studied municipalities falling below 15.

Ismail et al. (2022) initially found that rainfall data obtained from the Meteorological Department based on their weather stations (secondary data) showed insignificant results. Then they devised a rainfall data collection system based on IoT (Internet of Things) devices, placing several rain gauges (mobile weather stations) in the dengue hot spot areas, thereby enhancing the quality of the rainfall data, and potentially increasing the accuracy of the dengue outbreak forecasting model. Hence, rain gauges were placed between themselves at an average distance of 5 km. This is equivalent to distribute uniformly 10 weather stations within each 50 square kilometers’ radius; in Fortaleza, whose area is around 320 km², the Meteorological Department (FUNCEME) has only 4 rain gauges, whose data were used in this study.

Moreover, Ismail et al. (2022) distributed around each station an average of 4 ovitraps, which enabled them to establish deep understanding regarding the relationships among life cycle of mosquito Aedes aegypti larvae, climates variable, including rainfall, humidity, temperature, and the corresponding effects on dengue cases. All this information became input to develop a machine learning model based on Random Forest method, which constructs multiple decision trees with bootstrap aggregation method. This model provided predictions for forecasting dengue outbreak in Malaysia with 92% accuracy.

1.2 Findings in Brazil

Scandar (2007) carried out a study on cases of dengue in the city of São José do Rio Preto, state of São Paulo, Brazil from 1990 to 2005. Performing statistical analysis of Pearson’s Correlation for the incidence rate of dengue in relation to the following variables: age group, gender, income, schooling, rainfall, temperature, and presence of containers such as water tanks, vases, cans, tires, etc. in the environment. The study reports that in 2001, transmission began in prime areas of the city, where the cultivation of bromeliads (Bromeliaceae) was encouraged by landscapers in that period. That year, the transmission of the virus affected approximately 7000 people, being the biggest dengue epidemic that the city had ever faced in its history.

Amaral, Vaughon, and Duarte (2009) used the Box & Jenkins (1970) modeling methodology to develop an ARMA (Autoregressive-Moving-Average) model capable of making predictions of dengue cases based on the history of time series of dengue cases, temperature, and rainfall in the city of Rio de Janeiro from 2002 to 2008. The results showed that the variable temperature was not statistically significant, a fact that was considered as expected since the temperatures in the city of Rio de Janeiro as well as in Fortaleza are throughout the year within the ideal ranges for the eggs of the transmitting mosquito to hatch.

The surprising result of this study was that the model showed a relationship with a negative sign for the rain variable, suggesting that the years in which there was an increase in dengue cases were not the rainiest, but those that had a slightly lower amount of rain than historical average rainfall. The authors exemplify this conclusion with the year 2001, which was an epidemic year, and which had a rainfall index admittedly below the average. This conclusion deserves some credit since it is plausible to conceive that many Aedes aegypti eggs are lost in the sewer networks because of several consecutive episodes of torrential rain. However, two points must be considered:

First, the traditional way of measuring the average rainfall of a given year, that is, measuring its average rainfall from January to December, does not fit well with the phenomenon under study, that is: rainfall determining a favorable environment for hatching of Aedes aegypti eggs, and therefore determining a certain amount of dengue cases, which, in Brazil, swarm from summer to autumn, between the months of February and May in most states, or between the months of November and May in some others - mainly the ones located in the Amazon region. Rio de Janeiro, as well as Fortaleza, belongs to first group: there, dengue cases at the beginning of the year are to some extent determined by the rains of the previous year, and have a cumulative effect. From what we can conclude, therefore, when you want to calculate the rainfall average for a given year in order to know the amount of rainfall that caused dengue cases in that same year, you should ideally consider the initial and final months of this average respectively the month of the last year corresponding to the month immediately following the end of the current year’s outbreak, and the final month of the current year’s outbreak. This was the procedure we adopted to determine the annual rainfall averages presented in Tables 2 and 3 of this work.

Table 2
Biggest cumulative percentage difference in years with insignificant dengue outbreak.

Year	2020	2019	2010	2013	2007	2014	2021	2016	2018
Start week	13	12	46	22	16	20	18	15	10
Biggest six-week cumulative percentage difference of dengue cases (%)	22.56	23.03	23.30	24.19	26.54	30.23	34.80	36.71	38.11
Cumulative percentage of rainfall before start week (%)	43.87	40.17	93.47	65.21	53.55	73.44	60.47	67.26	29.21
Average weekly rainfall (mm)	53.24	39.48	12.03	21.50	24.82	31.17	42.43	47.73	29.79

Table 3
Biggest cumulative percentage difference in years with significant dengue outbreak.

Year	2011	2017	2015	2008	2009	2012
Start Week	11	11	16	15	7	16
Biggest six-week cumulative percentage difference of dengue cases (%)	42.90	46.20	47.92	51.61	52.18	62.23
Cumulative percentage of rainfall before start week (%)	52.96	40.06	54.01	41.74	9.05	58.57
Average weekly rainfall (mm)	45.86	31.56	36.96	34.86	24.50	39.04

Second, the preceding conclusions may have been induced by the fact that the authors modeled the rainfall time series through a model of moving averages of size 12 (months), which means that “only” the Trend component was modeled. As will be seen later, in this study, we modeled both the time series of dengue cases and the rainfall through SARIMA (Seasonal-AutoregressiveIntegrated-Moving-Average) models, a model that also adopts the Box & Jenkins methodology.

Sousa et al. (2016) analyzed the impact between socioeconomic and environmental factors concerning cases of dengue in Ceará districts over the period of 2002 until 2012. For this study a panel regression model data was used, with the variables: endemic disease control agents, domestic water supplies, basic sanitation, rainfall, municipal GDP (Gross Domestic Product) and health units. In this study the endemic disease control agents seems to be one of the most important tools against dengue outbreaks.

Santos et al. (2021) sought to analyze the influence of climatic factors (rainfall and ambient temperature) on the incidence of cases of Dengue, Chikungunya and Zika Virus for the municipality of Manaus, State of Amazonas, Brazil. To reach this goal, firstly, the ARIMAX method was used, which is a multivariate ARIMA model, proposed by Box and Tiao in 1975. It allows the analysis of more than one variable correlated to the prediction of a dependent variable, with a view to developing a forecast analysis of the three diseases, for the next 18 months. Subsequently, the authors estimated a Vector Error Correction Model (VECM, using the Johansen’s methodology, 1991) to verify the effect of climatic variables, maximum temperature, and precipitation, on the number of cases of the three analyzed diseases. The period of analysis comprised the months of January 2017 to December 2020.

To establish the ARIMAX model, the authors had to, among other procedures, estimate the CCF (Cross-Correlation Function) between the monthly time series. The estimated model for dengue cases was an ARIMAX(p=2,d=1,q=1,r=2). The cross-correlation results indicated that both rain and temperature determine dengue cases in the city of Manaus one lag (one month) in advance. The authors also verified that the precipitation and temperature variables present positive and statistically significant signs, demonstrating that a 1% increase in these variables would cause an increase of 0.71% and 4.97%, respectively, in dengue cases in the city of Manaus.

Xavier et al. (2021) consider climate a significant factor in the temporal and spatial distribution of vector-borne diseases such as dengue. Thus, precipitation and temperature are regarded as major macro drivers of dengue, as they directly affect the population density of Aedes Aegypti, which is subject to seasonal changes primarily because of these variables. In this study, the incidence of dengue in the metropolitan region of Rio de Janeiro, Brazil, was studied in relation to the climate utilizing remote sensing data on temperature and precipitation variables gathered from artificial satellites. The best-fitting mathematical model was an autoregressive moving average with exogenous inputs (ARMAX). This model was able to reproduce the incidence rates seen throughout the study period and to accurately anticipate the number of dengue cases in humans over one year.

Although climatic variables are often the most relevant in predicting the number of dengue cases, other non-climatic variables may, in some contexts, prove to be the most determinant ones. Such variables were not added to the models developed in this study, but it is worth including them in this literature review to remember that in some cases the non-adherence of mathematical models may be due to their absence.

This article presents a portion of a study on the behavior of rainfall averages and dengue cases in Fortaleza, Brazil, from 2007 to 2021. In this study, we aim to corroborate the direct relationship between the evolution of rainfall and dengue in the city, as proposed by Negreiros et al. (2011), by identifying the outbreak moments of the disease based on knowledge extracted from this behavior analysis using analytical graphics.

The data on dengue cases were obtained from the website of the Fortaleza City Hall, Health Surveillance Secretariat SIMDA (Daily Disease Monitoring System) (PMF, 2022), and the data on precipitation were obtained from the website of FUNCEME - State Foundation of Meteorology and Water Resources (GCE, 2022).

First, measurements of cross-correlations between the two random variables that represent the underlying stochastic processes were derived from empirical and visual analysis of joint graphs of the two-time series comprising the data under study. Through the conclusions of this double analysis, we sought evidence of two moments: the initial moment from which the accumulation of rainfall determines continuous increases in dengue cases, and consequently, the onset moment of outbreaks of arboviruses, which represent a moment of unbridled population growth of dengue vectors, causing an uncontrolled increase in the number of cases to the point of seriously undermining the installed capacity of local hospitals and emergency medical services, or even leading this health system to a temporary collapse.

This paper is divided into four sections, with section 2 describing the methodology used and section 3 presenting the computational results obtained using the R software (R DEVELOPMENT CORE TEAM, 2022) and the graphs generated from the data compilation. In section 4, conclusions and recommendations for future research based on the results are presented.

2 METHODOLOGY

From the rainfall data obtained from 7 rain gauges scattered in the city of Fortaleza (at Fuceme, Parquelância, Mondubim, Água Fria, Castelão, Pici and Messejana¹), collected daily and accumulated by average of the rain gauges by week according to the epidemiological weeks² of dengue control of Fortaleza/CE, and the data regarding the number of confirmed cases of dengue in the city by epidemiological week, this research composes two time series, which are analyzed, aiming to build two causal reference values, which intend to establish both a model for understanding and tacit knowledge of the process of dengue evolution in Fortaleza/CE.

The first causal model presents, by epidemiological week, the percentage of accumulated rainfall in relation to the total average rainfall of the city. The second model presents the percentage of accumulated dengue fever in relation to the total amount of dengue in the city of Fortaleza.

The view chosen to provide a better sensitivity in analyzing the proposed models was to compare just two years rather than the entire 15-years curve. Therefore, we were careful to choose meaningful years: 2012 was the first one chosen because it was the penultimate and worst epidemic year in Fortaleza (PMF, 2017; Magalhães et al., 2019; Oliveira et al., 2018); to establish a contrast, the other year chosen was 2013, when only an insignificant outbreak was registered. In order, models will reveal the relationship with respect to precipitation between these two years so disparate in terms of dengue cases. However, after those comparison it is plotted separately all 15-years cumulative curves.

To corroborate the observations arising from these models, the cross-correlations between the time series represented in the graphs are calculated more specifically, between the two random variables that represent the stochastic processes underlying the time series studied.

The cross-correlation technique is quite like the common correlation estimation (Pearson coefficient). However, when dealing with time series, it is necessary to isolate the correlations arising from trend and seasonality effects; otherwise, they would introduce spurious correlations in the cross-correlation calculation. In other words: for the correct application of cross-correlation it is indispensable that it be applied to stationary time series. Then, it is applied the technique known as pre-whitening (Costa, 2020), which consists in modeling the time series involved through the Box and Jenkins methodology (1976, apud Morettin; Toloi, 2006). After that, the crosscorrelation between the residues of the respective models is calculated. These are stationary, and representative of the stochastic processes of the original time series.

Significant and positive correlations existing at a given moment (lag x), indicate the number x of weeks that separate the leader or causal random variable that one that determines the cause of the phenomenon and the dependent random variable the one that suffers the effect (Fagundes et al., 2021). In the present case, the causal random variable is given by the stationary residuals of the rainfall time series, and the dependent random variable is given by the stationary residuals of the dengue cases time series. The phenomenon under study is the outbreak of dengue cases, determined by the magnitude, significance, and positivity of the correlations x weeks prior to the event, between the two aforementioned random variables.

The statistical software R was used to perform the calculations of cross-correlations and graphical plotting of the visualization results of each observation conducted here, which reflect the causeand-effect model under investigation.

The equating of these models in a single visualization shows us the average time for dengue events to occur simultaneously to the same percentage of rainfall, thus repeating the evaluation of Negreiros et al. (2011) on the systematic behavior of dengue in relation to the amounts of rainfall, and the clear identification of outbreak moments of the disease in the city, which can be mitigated by the coordinated action of endemic agents of dengue control.

3 ANALYTICAL RESULTS

To begin this presentation of data, Figures 1 and 2 show the absolute values of the two time series studied in this research: average rainfall in millimeters, and units of dengue cases, in the city of Fortaleza/CE, for the period 2007-2021. The average value for the period of each time series was highlighted with a horizontal line. In Figure 1 it is already possible to see an important characteristic of the rainfall in Fortaleza: the time of the year with the heaviest rainfall is composed of the months of February through May. This period is known as the “rainy season” of Fortaleza and in our time, scale corresponds to the period that goes approximately from epidemiological week 5 to week 22 each year.

Figure 1
Rainfall absolute value in millimeters, in Fortaleza/CE 2007-2021.

Figure 2
Number of dengue human cases in Fortaleza/CE 2007-2021.

It is interesting to note in Figure 2, that the period of the year when the highest number of dengue cases occurs is approximately coincident with the aforementioned rainy season, so that in these first two graphs it is already possible to see that the two-time series studied have a remarkably similar seasonality.

In Figures 3 and 4, we present the percentage graphs of average rainfall and dengue cases without accumulation for the city of Fortaleza/CE, for the period 2007-2021. In these figures, and in the rest of this work, we present the two-time series under study plotted together, providing a more adequate visualization for the graphs analysis. Ratifying what was said before, we can see that also in percentage terms the rainiest weeks in the city of Fortaleza/CE belong to the rainy season. In addition, in most years within this period there is one or more subsequent weeks in which it rains individually in each of these weeks approximately the equivalent to 5% of all the rain observed during the year³. This characteristic further emphasizes the irregularity of rainfall in the city irregularity observed in the rainy season in relation to the annual period, but also observed within the rainy season itself. In addition, we draw attention to the fact that the weekly percentages of dengue cases (in red) seem to follow closely the variations in rainfall percentages (in blue), although with a certain time lag, as we see better in the following graphs.

Figure 3
Weekly rain percentage (blue)/Dengue human cases (red) 2007-2021.

Figure 4
Weekly rain percentage (Blue)/Dengue Cases (Red) 2012-2013 (local expansion).

To evaluate it more closely, in Figure 4, the same curves already plotted in graph 3, only for the years 2012 and 2013, offer a broader local view. Note that after the first week with rainfall above 5% of the total rainfall for the year (blue curve) which is followed by others with the same characteristics after a certain lag, we begin to observe an increase in the slope of the curve of dengue cases (red curve), revealing the beginning of the “outbreak” movement. From what we could observe, this lag period can vary from 2 to 6 weeks.

In the year 2012 a year of well above average rainfallthis lag period was 2 to 3 weeks: the first week with rainfall above 5% was week 7, and already in week 10 we can see a subtle change in the slope of dengue cases. A little later, we can observe that in week 13, it rained almost 15% of the year’s rainfall; and already in week 15 we can see that the slope of the dengue curve has practically doubled a lag of only 2 weeks.

For the year 2013 a year with slightly below average rainfall the lag period was 4 to 6 weeks: the first week with rainfall above 5% was again week 7, but only from week 12 to week 13 is it possible to see a change in the slope of dengue cases. A little later, in week 16, when rainfall above 5% returned, the observed lag was about 4 weeks, with a new change in the slope of the dengue cases curve occurring from week 19 to week 20.

In Figure 4, we can also see that a week in which it rains about 5% of what is observed in the whole year can be classified as a week of heavy rain. It seems reasonable to infer that after a week of heavy rain, the probability of standing water being present in residences and public places in the city tends to increase. This inference coupled with the already known fact that the development period of the Aedes Aegypti mosquito to the adult stage ranges from 7 to 10 days (FIOCRUZ, 2019) i.e., from one to less than two weeks, seems to suggest that the delay observed in the previous paragraph (from 2 to 6 weeks) is both concise, and sufficiently comprehensive to explain the development and maturation of the first mosquitoes, followed by their first bites (from one to two weeks), and the appearance of the first symptoms of dengue. This period, according to the Secretariat of Health of the State of Rio de Janeiro (2021), lasts one week on average, but it can reach up to two weeks.

From this data, it also seems reasonable to infer that in years with above average rainfall such as 2012, for example there is a tendency for a decrease in the curves lag, suggesting that more torrential rains promote more favorable conditions for the development of the Aedes Aegypti with a higher presence of regions with standing water.

In Figure 5 we see the cumulative behavior of the percentage of average rainfall and of the dengue number of cases over the years 2007-2021.

Figure 5
Weekly percentage yearly cumulative rainfall (blue)/Dengue cases (red) 2007-2021.

Now, taking the same view in the years 2012 and 2013 regarding the cumulative percentage behavior, we can see very closely the difference in dengue cases between two years with very unequal rainfall volumes as it was the case in these two years.

In general, Figure 6 provides us once again with a portrait of the irregularity of rainfall in the city of Fortaleza/CE: we can see that both in years of above average rainfall (as it was the case in 2012), and in years of below average rainfall (as it was the case in 2013), approximately 80% of all rainfall for the year falls within the rainy season. However, an important difference between these two years seems to be in the speed with which precipitation accumulates within the rainy season.

Figure 6
Weekly percentage yearly cumulative rainfall (blue)/Dengue cases (red) 2012-2013 (local expansion).

In the year 2012, the accumulation of rainfall exceeds 50% already in week 13, and it is precisely at this point that the dengue cases curve steepens exponentially, characterizing a remarkable outbreak that takes the accumulation of dengue cases this year from a modest 20% in week 15 to an impressive 80% in week 21 that is, in just one and a half months.

In 2013, however, rainfall accumulation was milder, that is, the irregularity characterized by torrential downpours within the rainy season was smaller. By week 13 when in 2012 half of the year’s rain had already fallen it had rained only 25% of 2013 total rainfall. And half of 2013’s rainfall did not fall cumulatively until week 18 more than a month later than 2012. These characteristics seem to point out that 2013 was a less irregular year than 2012. We can see that coincidentally, just as in 2012, by week 15 the percentage of cumulative 2013 dengue cases were around 20%. But unlike in 2012, the cumulative percentage of dengue cases of 2013 only reached the 80% of cases of the year by week 32, i.e., it took about 17 weeks about 4 months while in 2012 this variation of accumulation from 20% to 80% only took a month and a half more than twice as fast. Note that the “outbreak” point occurs at the maximum variation.

Leaving now the comparison between years, and looking only at the comparison between the curves, we can also observe similarities and differences. In the year 2012, for example, we see that the rainfall curve reaches the 10% percentage accumulation in week 7, while the dengue cases curve reaches this percentage only in week 12, which is 5 weeks later. And we can observe that this time lag of about 5 weeks remains practically constant until the curves reach their 60% accumulated percentage. Until this point, that is, until week 19, dengue cases have a vertiginous growth, but in everything like that of rainfall minus the time lag of about 5 weeks. But after week 19, despite the rainfall curve slowing somewhat in its rise, the dengue curve continues its exponential climb, characterizing the “outbreak” - a moment of uncontrolled dengue cases - while it represents a moment of independence of the dengue curve in relation to the rainfall curve. So impressive is this moment that in just one week from week 19 to week 20 cumulative dengue cases rise from 60 to 70%; and just one more week is enough for cumulative cases to reach 80% of all 2012 dengue cases by week 21.

Thus, we can once again infer that during a certain period within the rainy season, environmental conditions favorable to the population of Aedes Aegypti expansion are gradually developed and accumulated, especially by the rains, in the form of standing water throughout the city. This period, supposedly of “incubation”, lasts from approximately week 5 (when the rainy season begins) until weeks 18 to 19, when the curve of dengue cases acquires an exponential slope, exceeding the growth rate of the rain curve, and characterizing the “outbreak”. It is worth remembering that before this moment of inflection, the two curves follow together at a very similar growth rate for about 6 weeks, a period in which the accumulated percentage magnitudes of the two curves are virtually identical, except for the time lag of about 4 to 5 weeks, with the curve of dengue cases always lagging behind that of rainfall, and therefore possibly determined by it to some extent.

To finish this analysis of the cumulative percentage value graphs, let us once again look at the curves under study for the year 2013. Unlike what occurred in 2012, in 2013 there does not seem to have been such an uncontrolled “outbreak”. As we know, in 2013 the rainfall within the rainy season did not have as many torrential episodes or as we called it at the beginning of this article: as many “weeks of intense rainfall” as in 2012.

This break in rainfall irregularity, though subtle, seems to have promoted the maintenance of the temporal lag at a constant level throughout 2013; a lag of 5 to 6 weeks between the accumulated percentages of rainfall and dengue cases. The maintenance of this lag as a constant may be suggesting that this period of 5 to 6 weeks is a reasonably adequate period for the population of Fortaleza to adopt sufficient preventive care for the maintenance of Aedes Aegypti populations at controlled levels, i.e., further away from the possibility of an “outbreak”. At the same time, the smoother slope of the graph of accumulated rainfall percentages in 2013 seems to suggest that this level of accumulated rainfall percentage growth within the rainy season does not reach the point of causing environmental conditions so favorable to Aedes Aegypti uncontrolled population explosion a situation that seems to have occurred in 2012. One cannot also neglect the work done by the endemic disease agents this year, as their intensity at this time may have influenced in the sense of greatly mitigating the effects of the Aedes Aegypti in the population of Fortaleza.

Complementing the analysis done so far, we present below the cross-correlation calculations of the two-time series under study. The pre-whitening process resulted in the following models: for the rainfall time series, a SARIMA model (9,0,3) (0,53,1); and for the dengue cases time series, a SARIMA model (38,0,0) (0,48,1). The normality of the residuals of these models was verified by applying the Shapiro-Wilk statistical test, resulting in p-values 0.277 and 0.059, respectively. The application of cross-correlation in R language is done by calling the ccf() function. The command performed was: ccf (va rainfall, va dengue cases, ylab=“Correlation”, main=“Cross Correlation Rainfall--+Dengue”), where the first parameter is, by hypothesis, the causal random variable, and the second, the dependent random variable. The results can be seen in Figure 7.

Figure 7
Cross correlation Rain/Dengue 2007-2021.

The interpretation of Figure 7 is as follows: the significant cross-correlation values (with value greater than the confidence interval⁴ demarcated by the two blue dashed lines) were observed at negative lags. This indicates that the hypothesis that the causal random variable is indeed the one that was entered as the first parameter of the ccf function was correct, i.e., it is indeed rainfall that causes effects on dengue cases. If the significant autocorrelations were in positive lags, the conclusion would be the reverse. Furthermore, we can observe that the autocorrelation of greatest magnitude occurs at lag -2 with magnitude 0.753, that is, for most of the history of the two ST’s the increases (positive correlations) of the two random variables occurs with a lag of only 2 weeks. But we can also observe that there are significant correlations in lags -1, -3 and -4, that is: rainfall determines up to 4 weeks in advance the cases of dengue in Fortaleza in the period studied, which statistically corroborates the observations made earlier, through visual analysis on the graphs of weekly percentage and cumulative percentage of rainfall.

We finish this section plotting in Figure 8 separately all 15-years percentage cumulative rainfall (in blue) and dengue cases (in red) graphics. Those marked with only one red asterisk are years in which significant outbreaks occurred; while those marked with two red asterisks are epidemic years. Following the steps already traced in the previous analyses, an outbreak point was considered the point at which an increase of more than 40% was observed in dengue cases during the preceding six weeks. Tables 2 and 3 below have ordered by six-week cumulative percentage difference in dengue cases, and were generated by R Scripts. They summarize information about the major outbreaks of dengue cases recorded in a contiguous set of six weeks in each year, the week in which accumulation began, the amount of accumulated rainfall since the beginning of the year under study, and the average rainfall in the corresponding year. Epidemic years are those in which outbreaks occurred, and moreover, they were considered as such by the City Hall of Fortaleza (PMF) due to the extremely high number of absolute cases of dengue observed. Since 1986, the PMF has cataloged the following years as epidemics: 1994, 2008, 2011, 2012 and 2015 (PMF, 2017). In addition, the historical annual average of rainfall per week in the city is 34.33mm.

Figure 8
Separately percentage yearly cumulative rainfall (blue)/Dengue cases (red) 2007-2021.

Table 3 shows that in 2012, the biggest cumulative percentage difference between 6 consecutive weeks is started in week 16 and computes 62.23%: this is the maximum six-week outbreak in 2012; however, it is appropriate to remember that in week 13 a difference greater than 40% are already registered. Another interesting observation presented in Table 3, is that the biggest outbreaks started, on average, in week 13, and up to this point, it has accumulated about 50% of the year’s rainfall, which is only possible in years characterized by several torrential rains since the first weeks of January. The year 2009 represents an outlier as it can already be deducted from its average rainfall; since cumulative dengue cases are represented as a percentage, 52.18% represents indeed a large, but relative increase; in absolute terms, the highest number of dengue cases in 2009 was 449 in week 10, while in week 17 of 2012 we had 2909 cases.

To identify the exact instant of an outbreak, we considered the Instantaneous improvement between k consecutive weeks. In this method we consider the number of cases in actual i-th week minus the number of cases in the (i-k)-th week, and obtain a bar graph containing the instantaneous information.

In Figure 9 it can be seen the bar graphs representing the graphs the years 2007-2019, and the indication of the provable outbreak points of that year and the discarded outbreaks for other years because of unclear definition of the event behavior. This method is easy to understand and functional although its fragilities and conceptual decisions behind the existence of a sudden outbreak point. The suggested outbreak moment is indicated in black bars in the graph referring to a sudden change of values between [3.5-10] times the previous week in two-three consecutive weeks. Note the constant occurrence of this behavior in the epidemiological weeks as marked in black in annual bar graphs presented in Figure 9. It most frequently occurrence in week 14 with two weeks (12-13) back and forth (15-16). Curiously we also have in the graph the representation of the reversion of the outbreak (fast instantaneous decrease of the number of cases) along the years.

Figure 9
Instantaneous improvement bar graphs - Dengue in Fortaleza: 2007-2019.

4 CONCLUSION

As much as irregular rainfall favors dengue, it is undeniable that preventative human actions are crucial in mitigating its uncontrollability. To endemic disease control services to operate with a reasonable degree of confidence and efficacy, the identification of disease outbreaks is indispensable. This study demonstrates, via a causal model, that precipitation and dengue cases occur in a manner that can be identified by percentage relationships and sharp variations in measurements. Such variations are indicative of “outbreaks”, which can be detected in Fortaleza by rainfall between the fifth and ninth weeks of the epidemiological year, with a sharp increase in dengue between the twelfth and thirteenth weeks.

As much as precipitation expands natural habitats for the development of the Aedes Aegypti mosquito, the preventative efforts of the population contribute to their reduction. Eliminating standing water in their own homes is a simple act that has a significant impact on reducing the growth of the mosquito population carrying dengue.

This study focused on the quantitative aspect of the relationship between the time series of rainfall and dengue cases, which appear to be equally capable of exerting a determining force in the composition of causes and effects that may lead to an outbreak of dengue in Fortaleza/CE.

Thus, the findings of this study quantifiably and implicitly support the claims of Negreiros et al. (2007) regarding the correlation between the evolution of precipitation and the evolution of dengue cases in Fortaleza/CE.A relationship that is not only direct, but also quite intimate, as demonstrated by the seasonal behavior of the two time series under study, as well as by the occasional changes in trends of the rainfall time series, all very closely accompanied by corresponding changes and always positively correlated by the series of dengue cases in such a remarkable manner, that we can almost say in a clearly figurative sense that the time series of dengue cases is constantly riding on the back of the time series of rainfall.

The literature review revealed that there are still few works that use CCF to establish the magnitudes and the advance with which climatic variables determine dengue. Even among the most recent articles searched, it was difficult to find such a line of research. Of the various articles surveyed, only the one by Santos et al. (2021) used the CCF at a level that can be comparable to that used in the present work. Even the number of lags with which rain precedes its effects on dengue found by those authors (1 monthly lag) was equivalent to that found in this study (4 weekly lags).This aspect reveals an important innovation of this study.

In contrast, the work by Amaral, Vaughon, and Duarte (2009) mentions CCF, but does not present the quantification of the cross-correlation between rainfall and the incidence of dengue cases. Perhaps the fact that these authors found negative correlations between rainfall and the incidence of dengue cases in Rio de Janeiro is linked to their lack of rigor in establishing the CCF; because, if the correlations are collected in the same lags of the two time series, it is natural that the correlations between the variables are negative, whereas, as we found in this study for the city of Fortaleza, if the rainfall variable is collected around 4 earlier weekly lags with respect to the lag of the dengue cases variable, positive correlations will be found.

Furthermore, this research has led us to an additional significant conclusion: the practical applicability of the study’s findings. A potential application, which suggests to the authors a unique opportunity to expand upon the current research, would be a Webdengue Framework⁵ auxiliary algorithm, which could be described in general terms as follows.

First, generate a forecast one or more weeks in advance, based on a static ARIMA or SARIMA model that is periodically revised. This forecast could be derived from either the time series of rainfall or the time series of weekly dengue cases both of which are presented in this study or a combination of the two.

Then, similar outcomes should be sought in preceding and subsequent time series windows. Each corresponding window must be saved as a reference.

In the next step, the results of the search described in the preceding paragraph would be sent in a compatible file format (such as JSON)to Webdengue’s Dynagraph Module (Chaves, 2007). (Graphvs, 2022).

With these outcomes, Dynagraph can execute the DBScan/IGN algorithm on the moving averages of the data sent by this forecasting module, which could be implemented in R, for example.

Currently, Dynagraph executes this algorithm, but through moving averages over the four weeks prior to the current week, generating from these data, a geospatial instance for the DBScan/IGN algorithm to assemble the groups of predicted dengue cases for the next future week, presenting them visually, in georeferenced maps, considerably easing the interpretation of the prediction data, and decision-making.

As reported in the conclusions of Chaves (2017), Dynagraph’s success rate during periods of low dengue incidence in the city of Fortaleza-CE was only 20%. These times are optimal for educational campaigns to eliminate outbreaks of stagnant water, making them equally important in the fight against Dengue, which is an ongoing effort. To provide decision-makers with the ability to focus educational efforts on a specific geographical area that is more likely to be affected by stagnant water outbreaks in the coming weeks, it is desirable for Dynagraph to be able to make highly accurate predictions even during these times.

If, instead of applying the moving average model of DBScan/Dynagraph to the spatio-temporal data mentioned in the previous paragraph, we applied it to weekly seasonal windows of the same characteristics in previous years, determined by forecasts of ARIMA or SARIMA temporal models, as suggested by this work, could we obtain better performance in the forecasts of Dynagraph Webdengue Framework’s spatio-temporal forecasting module? The answer to this question will be found in future research that will expand upon the studies and findings of this work.

Finally, it is opportune to consider that the conclusions reached by this work lead its authors to consider some inevitable logical developments, which may be subjects of future investigations. For example: since it is argued that there are correlations between rainfall and the occurrence of outbreaks of dengue cases, and since this correlation is strongly based on the support that stagnant water gives to the life cycle and proliferation of the mosquito that transmits dengue, it seems plausible, to raise hypotheses that relate the accumulation of water with certain elements of the urban infrastructure, and as an indirect consequence, determining to some extent the growth of dengue cases; works that did something similar to this were Martheswaran et al. (2022) ’s and Scandar (2007)’s, referenced in the literature review.

Similarly, changes in the social behavioral patterns, for example, those referenced by Scandar (2007), or the ones caused by the recent COVID-19 pandemic could reveal new independent variables determining the growth of dengue cases, and the occurrence of outbreaks. Table 2 has shown that years 2019, 2020 and 2021 had enough potential to generate large outbreaks. Could the pandemic have influenced this number? It should also be considered that since the last epidemic, in 2015, the actions of agents to combat endemic diseases in the city of Fortaleza have become increasingly efficient; could such actions have influenced the decrease in outbreaks in these years? If we consider the conclusions of Sousa et al. (2016), the answer seems to be yes.

It is important to note that we are dealing with a living dynamic system, frequently changing. So, the composition of local history that determines local outbreaks can be altered by new significant points emerging from new facts, or even old hypotheses that have been poorly explored to date.

Acknowledgements

We would like to thank the anonymous referees for their kind work that improves this article. We thank CNPq, for the PIBIQ-UECE program to graduate students, that supported this research. Finally, we would express our full gratitude to professor Airton Fontenele Sampaio Xavier (in memoriam) to indicate us the dengue outbreak detection challenging.

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• 1
  Of these posts, the first four are now inactive, having contributed data for this research only in the years 2007 and 2008.
• 2
  Epidemiological weeks always start on Sundays and end on Saturdays. The first epidemiological week of the year ends, by definition, on the first Saturday in January, as long as it falls on at least four days in the month, even if this means that the first week begins in December, so that we can have years with 52 or 53 epidemiological weeks. For the sake of simplification and aiming for greater homogeneity among the annual time series periods, in this research all years were considered as having 52 weeks, with any data belonging to week 53 being accumulated in week 52.
• 3
  In some years we can also observe the occurrence of weeks when it rains - in a single week - more than 10% of all the rainfall of the year. However, this situation is very rare, and seems to arise only in those years when the rainfall volume is above the historical average values, and therefore when the rainfall irregularity is greater than the “normal” one.
• 4
  This value is automatically calculated by the ccf function. In this case it was calculated at+/- 0.54.
• 5
  Computational framework to support the fight against dengue developed by Negreiros (2002) that includes mobile appli- cations to support notification for preventing and fighting dengue, besides an Operations Research module for organizing and optimizing teams and tasks, and a spatial-temporal forecasting module called Dynagraph to support early decision making.

Publication Dates

• Publication in this collection
  19 Aug 2024
• Date of issue
  2024

History

• Received
  31 Jan 2023
• Accepted
  15 May 2023