additional reports were also extracted from promed mail ( 8) and healthmap ( 9 ) . we performed the analysis by using 3 dates : 1 ) date of case registration in the surveillance system of the brazilian ministry of health ( model 1 ) ; 2 ) earliest of either date of symptom onset ( if available ) or registration date ( model 2 ) ; and 3 ) earliest of either case registration date , date of symptom onset , or date of case report by other sources ( model 3 ) . surface trend analysis was used to interpolated a continuous estimate of disease spread speed in magnitude and direction ( 10 ) by using available spatial and temporal information . time of dispersal was calculated from the start of the epidemic for each model ( technical appendix ) . data provided by the brazilian ministry of health on may 31 , 2016 , indicated that zika had been confirmed in 316 of 5,564 municipalities in 26 states ; 6 additional municipalities were identified from other reporting sources . contour maps of interpolated temporal trends ( figure 1 ) indicate a trend of spread into southern and western brazil , and initial outbreak reports originated from municipalities along the northeastern coast . on the basis of confirmed cases , the earliest location of spread was the northeastern coastal area between the states of paraba , cear , baha , alagoas , and rio grande do norte . there were also earlier dates of self - reported symptom onset in the northwestern state of amazonas ( january 1 , 2015 ) , the west - central state of matto grosso ( january 4 , 2015 ) , and the southeastern coastal state of rio de janeiro ( january 1 , 2015 ) . contour surface trends and directional vectors for reconstructing zika introduction in brazil . a ) date of case registration ( model 1 ) ; b ) earliest date between date of symptom onset ( if available ) and date of registration ( model 2 ) ; c ) earliest date between date of case registration , date of symptom onset , and date of case reporting by other sources ( model 3 ) . each contour line represents a 1-day period , and contour lines farther apart show that the disease spread rapidly through an area , whereas lines close together show slower progression in an area . . magnitude of speed and direction should be interpreted cautiously near the edges of the study area . estimates of speed are subject to edge effects , which indicates that estimates are less stable because they are based on fewer data ( not as many neighboring values ) . contour maps ( figure 1 ) indicate slight differences in patterns of dispersion between the models . model 1 indicates the strongest trend of a southward spread from the northeastern coast toward the populous southeastern coastal states of rio de janeiro , esprito santo , and so paulo ; the estimated time of dispersal was 22 weeks ( figure 1 , panel a ) . in addition to west to east spread of zika in southern brazil , there was a pattern of movement west toward bolivia . the dispersal trend for model 2 was more varied but also indicated spread to the southeastern coastal states of rio de janeiro , esprito santo , and so paulo ( figure 1 , panel b ) . this model also suggests an initial spread north from the earliest reports in the northeastern region and a spread west toward bolivia . model 3 suggests a strong southward spread originating from the northeastern coast toward the southeastern coastal states ( approximate dispersal time of 29 weeks ) and toward the western border and northwestern state of amazonas ( figure 1 , panel c ) . overall , the average speed of diffusion was 42.1 km / day or 15,367 km / year . the minimum speed across all 3 models was 6.9 km / day , and the maximum speed was 634.1 km / day ( figure 2 ) . municipalities in northeastern and northern regions had the slowest speeds , and municipalities in the west - central and southeastern regions had the highest speeds . more cases occurred closer in time and over larger areas in southern , southeastern , and west - central regions , which resulted in faster rates of case introduction . speed or log speed ( km / d ) of zika introduction into municipalities in brazil . a ) june 2015may 2016 ; b ) january 2015may 2016 ; c ) january 2015may 2016 . gray circles indicate central  western region , green circles indicate northern region , light blue circles indicate northeastern region , black circles indicate southern region , and dark blue circles indicate southeastern region . all models were consistent in agreement that zika dispersal in brazil followed a general pattern of southward spread toward the populous coastal states ( average speed of introduction of 42 km / day ) , which could be explained by multiple introductory cases into different areas probably caused by movement of viremic persons . we estimate that it took 56 months for zika to spread from the northeastern coast to the southeastern coast and western border of brazil . these findings are supported by the first report of local transmission of zika virus in paraguay in late november 2015 ( 11 ) and in bolivia in january 2016 ( 12 ) , 7 months after the first registered case in brazil . limitations of this analysis include quality and timeliness of surveillance data that provided the basis for this study . symptom onset date is subject to error because it is based on self - report , and earlier introductions of zika in some municipalities might not have been captured by the ministry of health surveillance system and supplementary data sources , given the mild and generic nature of zika symptoms and the high proportion of asymptomatic persons ( 3 ) . the northern region of brazil had a major dengue outbreak in early 2015 , and given symptom similarities between dengue and zika , it is probable that some suspected dengue cases were in fact early cases of zika . sporadic geographically disparate cases were recorded in various parts of brazil , which increased the uncertainty associated with speed analysis . these cases , such as those in northwestern brazil , increased uncertainty in direction and speed estimates , which are also related to edge effects . edge effects occurred along the boundary of the study area , which in this study were constructed by using fewer data points and are therefore less stable . this effect is shown with directional arrows pointing toward earlier areas of spread versus toward later areas of spread ( figure 1 , panels b , c ) . the arrival and rapid spread of zika virus in the americas resembles that of chikungunya virus , which was introduced into saint martin in the caribbean in 2013 ( 13,14 ) . increased knowledge of the speed of spread and direction of zika spread can help in understanding its possible future directions and pace at which it travels , which would be essential for targeted mosquito control interventions , public health messages , and travel advisories . future work will investigate underlying causes for the southward and westward spread in brazil by incorporating mobility data and seasonal events , such as movement of persons between northeastern and southeastern regions for vacations , which could have driven the spatial transmission pattern . furthermore , multicountry analysis is needed to understand continental spatial and temporal patterns of dispersion of zika virus and co - circulating viruses , such as chikungunya virus .
we estimated the speed of zika virus introduction in brazil by using confirmed cases at the municipal level . 
 our models indicate a southward pattern of introduction starting from the northeastern coast and a pattern of movement toward the western border with an average speed of spread of 42 km / day or 15,367 km / year .