A spatio-temporal analysis of dengue spread in a Brazilian dry climate region

We investigated the relation between the spread, time scale, and spatial arrangement of dengue in Bahia, a Brazilian dry climate region, for the period 2000 to 2009. The degree of cross-correlation is calculated for 15 economic regions. We propose a multiscale statistical analysis to datasets of dengue cases in order to verify the effect of infection dispersal on the economic regions from the metropolitan region of Salvador. Our empirical results support a significant and persistent cross-correlation between most regions, reinforcing the idea that economic regions or climatic conditions are non-statistically significant in the spread of dengue in the State of Bahia. Our main contribution lies in the cross-correlation results revealing multiple aspects related to the propagation of dengue in dry climate regions.

Dengue, Zika virus and Chikungunya are caused by arboviruses that are transmitted in urban centers by the same arthropod vector, Aedes aegypti mosquitoes (AA). Once infected, the mosquito can transmit the virus during its whole lifetime. However, the course of an infection differs between people. The transmission of these arboviruses is complex, involving the various aspects of the vectors' behavior as well as that of the infected humans [1][2][3][4][5][6][7][8] . Studying the tracking and history of a disease has been a way to understand its behavior 9 . We believe that evaluating temporal interactions of case records may reveal relevant clues about the disease spread process, mainly in large areas. For instance, large cities can provide favorable conditions for arbovirus transmission due to the easy circulation of infected people. Spatial analysis has been able to construct scenarios and identify health impacts 10 . Studies involving spatial and temporal disease have tried to identify patterns of the dengue infection. For instance, spatial and temporal patterns of dengue infection were studied in two cities in Taiwan by applying cluster analysis and two distinct diffusion behaviors were found, a rapid dispersal and a relocation pattern of temporal movement involving clusters 11 . A study involving pattern the dengue patter and hemorrhagic dengue incidence in several districts was applied in the Songkhla municipality in Thailand. The findings revealed that the incidence was strongly associated with the percentages of shop-houses, brick-built houses and houses with poor garbage disposal 12 .
Brazil has natural features that make it vulnerable to arboviral diseases. In recent years, Zika virus and Chikungunya joined dengue as relevant Brazilian public health problems. As data on Zika virus and Chikungunya data are still scarce, using dengue data may provide important clues about their spread patter. Bahia is the fourth largest region of Brazilian in terms of population, with 14, 016, 906 inhabitants. Covering 564,732 km 2 , it has an extensive road network interconnecting all municipalities in the state 13 . Besides, Bahia has specific climatic conditions such as low precipitation, as shown in Fig. 1. The transportation network in Bahia consist of 22 federal highways and 11 state highways covering all 417 municipalities 14 . As AA is present in 99.5% of municipalities in Bahia, combating the spread of arboviruses is a challenge for public health.
With 1 high levels of precipitation and a temperature suitable for dengue transmission, there is a strong association with elevated dengue risk, although low precipitation was not found to limit transmission greatly. A study measuring the existence of a spatial correlation between socioeconomic, demographic and environmental variables and the incidence of dengue in a medium-sized city in Brazil, found spatial dependence of the incidence of dengue, socioeconomic factors and the organization of urban space 16 9,14,17 . Another study evaluated whether the spread of dengue fever can be explained by differences in regional economies, concluding that this disease was not influenced by economic aspects or regional arrangement, and also suggesting that the disease's AA vector has adapted to all economic regions 18 . The diffusion of disease may be observed as a complex system. Thus, Self-Organized Criticality (SOC) 9,19 , fractal behaviors 18,20 , non-linear systems 8 among other features could be useful in the analysis of spread of diseases. In relation to dengue, the transportation presents correlations among criticality, physical means of propagation, and distribution of dengue cases 17,21 . The fractal behavior presents correlation with SOC exponents 20 . In this sense, analyzing fluctuations allows us to verify features of the evolution of dengue that are not evident when we use traditional methods.
As there is no effective chemical and biological vector control, and the fact that no vaccine against dengue, Zika virus and Chikungunya are not yet available, the hypothesis of the pathways and speed of arbovirus circulation in Bahia-Brazil may be relevant factors to interrupt the spread of arboviruses. As time series of dengue are available, we propose to evaluate the speed and dynamics of the spread of the disease. To do so, we verify the pathways of dengue by applying the cross-correlation DCCA statistical method to dengue cases Bahia-Brazil between 2000 and 2009.

Results
We calculated 105 pairs for 29 different time scales, considering boxes from 4 to 362 days. Figure 2 shows the cross-correlations between RMS with all ER. The following regions presented a strong cross-correlation coefficient after 33 days: LTN, REC and PGU. A cross-correlation is considered strong when the ρDCCA is greater than 0.66 22 . All the other regions did not show a strong cross-correlation coefficient, but they are statistically significant, except IRC and BMF, which become non-significant after 154 days.
The pathways of the dengue spread are shown in Fig. 3. For better visualization of this spread, we proposed a classification for the coefficient degree, as follows: Strong: ρ DCCA > 0.66 , Medium: 0.4 < ρ DCCA ≤ 0.66 , Weak: 0.2 < ρ DCCA ≤ 0.4 , and Very weak: ρ DCCA ≤ 0.2 . This shows the continued strong correlation for ER around RMS borders for any time scale. Between 154 and 254 days, there is a weak to medium coefficient movement in almost all ER of Bahia that do not border with RMS, except for EXS, SGE, BMF and IRC. The spread remains unchanged after 254 days. This behavior may suggest that the spread directly associated with the distance between municipalities.

Discussion
The multiscale statistical analysis was applied to the datasets of dengue cases to determinate the effect of infection dispersal on the economic regions, starting in the metropolitan region of Salvador. It is the first time the ρ DCCA method has been used to assess the spread of dengue in a dry region of the world. The interaction of distinct economic units was observed the in Bahia from the metropolitan region of Salvador, with the apparent interconnection having the capacity to form the transmission chain, and hence the spatio-temporal spread of the virus.
The considerable increase of degree coefficient allowed determinate of the time scale dynamic of the spread of dengue in a dry region of Brazil, where in the begging the ρ DCCA coefficient becomes strong after 33 days for economic regions bordering RMS, as shown in Fig. 3. The co-movements provided by ρ DCCA has the advantage of setting aside local and regional details, such as economic aggregates, areas, and distances, giving an opportunity to evaluate the dengue propagation pathways and its dynamic.
The empirical results support a significant and persistent cross-correlation between most economic regions. These co-movements between economic regions and the metropolitan region of Salvador do not seem to be statistically impacted by the state's climatic conditions. The central region of the map, which is extremely dry (Fig. 1) and where the region number 5 is found, is strongly correlated with the metropolitan region (1) after 91 days.
Likewise, almost all economic regions have a medium or strong cross correlation with the metropolitan region of Salvador in the period of one year. Thus, we can conclude that the economic division defined by law No. 6,349 of the state of Bahia is not a significant barrier to the spread of dengue across the state from the metropolitan region of Salvador.
The scope of the study is limited to the state of Bahia, Brazil. Our main contribution lies in the co-movement results, revealing multiple aspects related to the propagation of dengue in these dry climate regions. Finally, the model has some level of uncertainty, an inherent limitation of the model assumption as a large time series. Other analysis, such as assessing municipalities individually and the impacts on neighborhood co-movements, may be easily implemented. Factors such as the spatial distribution of the transport network and the movement of people between cities can also be considered to analyze co-movements.

Methods
For better understanding the methodology applied, the schema of data analysis was provided in Fig. 4, where the daily records of dengue cases in Bahia were collected between 2000 and 2009 from the Brazilian Diseases Notification System databases (SINAN) from the Brazilian health ministry 25 . We note that the database used in this paper does not identify individuals and they were notified in urban areas. The dengue records were organized into Economic regions, an arrangement used by the Superintendence of Economic and Social Studies for the State of Bahia-Brazil (SEI-BA) and created by Bahia's low 6,349, which divides the State into 15 economic regions (see Table 1) 24 . The data on dengue cases data were aggregated in each economic region respectively. Figure 5 shows the map to assist understanding. The most important ER (RMS) was chosen in this analysis due to its economic importance and to include the capital of Bahia, Salvador. Furthermore, Salvador is classified as a Regional City of Influence 13 as showed in Fig. 6. Such cities are characterized by the intensity of the connections between cities cities. They play a role in territorial management, evaluating levels of centrality of the executive and judiciary at the federal level, and of corporate centrality, as well as the presence of different facilities and services.
The assumption of stationarity of random variables is required to perform many statistical inference methods. For instance, when we want to correlate distinct data sets in order to predict their behaviours, the non-stationary in the signals makes the standard Pearson correlation coefficient useless in the this hypothetical evaluation. Thus, it is necessary to use statistical models that develop to accommodate the complexity of the data. The detrended cross-correlation (DCCA) method can estimate the true correlation coefficient between series precisely 27 . This method is robust to contaminated noises, such as daily dengue records, and the DCCA methods have some advantages in correctly quantifying scale-dependent correlations 28 .
The ρ DCCA cross-correlaion coefficient method used is a proposal of 26 , based on the self-affinity theory (fractal object) 29 and the study of cross-correlation between time series defined by power laws 30 . In this context, there is some recent progress in cross-correlations method families, see 27,[31][32][33][34][35][36] . For the explanation how to calculate the ρ DCCA cross-correlation coefficient, see Supplementary Information, section S1.   24 . Among several arrangements, the SEI-BA provides the Economic Regions (ER) which is supported by Bahia's low # 6.349 24 . The ρ DCCA cross correlation analysis method 26 was applied at SINAN filtered data aggregated by ER.