Spatio-temporal dynamics of dengue in Brazil: Seasonal travelling waves and determinants of regional synchrony

Dengue continues to be the most important vector-borne viral disease globally and in Brazil, where more than 1.4 million cases and over 500 deaths were reported in 2016. Mosquito control programmes and other interventions have not stopped the alarming trend of increasingly large epidemics in the past few years. Here, we analyzed monthly dengue cases reported in Brazil between 2001 and 2016 to better characterise the key drivers of dengue epidemics. Spatio-temporal analysis revealed recurring travelling waves of disease occurrence. Using wavelet methods, we characterised the average seasonal pattern of dengue in Brazil, which starts in the western states of Acre and Rondônia, then travels eastward to the coast before reaching the northeast of the country. Only two states in the north of Brazil (Roraima and Amapá) did not follow the countrywide pattern and had inconsistent timing of dengue epidemics throughout the study period. We also explored epidemic synchrony and timing of annual dengue cycles in Brazilian regions. Using gravity style models combined with climate factors, we showed that both human mobility and vector ecology contribute to spatial patterns of dengue occurrence. This study offers a characterization of the spatial dynamics of dengue in Brazil and its drivers, which could inform intervention strategies against dengue and other arboviruses.

can be used to assess the speed of wave propagation for a particular period.

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The annual signal dominated in state level case series (individual power spectra for each state can be 113 found in S3-S5 Figs), and to explore it further we extracted phase angles for the annual component. The 114 next step was to obtain pairwise phase angle differences between states that indicate for each point in 115 time whether a state is ahead or behind another one in terms of recurrent annual waves. Consequently, 116 for each state we obtained the average phase difference from the other 26 states. The mean value of this 117 phase difference over time was used to produce a map of annual phase lags between states. Phase 118 differences were interpreted as time units as for the regular annual signal phase angle changes from -π to 119 +π in 1 year, which makes the phase lag of 1 radian equivalent to approximately 2 months. Hence, the 120 map of annual phase lags represents the average ordering of states in terms of dengue wave arrival times.

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Epidemic synchrony and annual phase coherence 122 We considered correlations between regional time series by computing the Pearson correlation 123 coefficient of raw case series (epidemic synchrony) and annual phase angles (annual phase coherence) for

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The exponents α, β and γ were estimated using a linear regression of the log-transformed form of the 149 original equation: We excluded data on region pairs for which we had negative correlations to allow for log-transformation.

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We used R 2 and Akaike's Information Criterion (AIC) for model comparison, and also generated 8 153 bootstrapped confidence intervals for the parameters by resampling the location pairs with replacement 154 500 times.

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Spatial resolution 156 We used different spatial data aggregation levels given that a large number of municipalities had very few 157 cases for certain seasons. We used three official administrative levels: state level (n = 27, 26 states and 158 the federal district Brasilia, hereinafter referred to as state), mesoregion level (n = 137) and microregion 159 level (n = 558). In addition, we performed our analysis using alternative Urban-Regional divisions

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Epidemic synchrony and annual phase coherence 204 We explored correlations between dengue time series in different regions. Both epidemic synchrony and 205 phase coherence were higher for closer regions and declined with distance (Fig 3). For the Urban-2 (n = 206 161) spatial level, epidemic synchrony reached the average countrywide correlation at approximately 207 1,260 kilometres ( Fig 3A). This synchrony length represents a substantial part of Brazil's dimensions as the 208 country extends 4,395 kilometres north to south and 4,319 kilometres west to east. The coherence length 209 had a higher value of 1,590 kilometres (Fig 3B), suggesting that agreement in dengue seasonality spreads 210 further than correlations of epidemic curves.

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We also looked at epidemic synchrony and annual phase coherence at other spatial levels (S4 and S5 Figs, 217 respectively) and found that both synchrony and coherence lengths tend to decrease for smaller spatial 218 resolutions and stabilise at 1,240 km and 1,500 km.

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Determinants of dengue epidemic synchrony and annual phase coherence 220 We built a suite of models investigating potential determinants of dengue epidemic synchrony (Table 1).

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The classical gravity model (model 4) that accounted only for distance and the product of population sizes 222 of regions captured a part of variation in epidemic synchrony (9.6%) which was higher than those of vector  We explored performance of the statistical models for other spatial levels (see Fig 4) and found that 236 overall model 8 (gravity model combined with precipitation) was the best in terms of variance explained.

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The classical gravity model (compared to climate factors) explained the majority of variance in epidemic 238 synchrony across most of spatial scales (Fig 4A). However, at smaller scales, precipitation contributed the 239 most for coherent timing of annual epidemics (Fig 4B).