Inferring the risk factors behind the geographical spread and transmission of Zika in the Americas
[['The proposed model is evaluated at a country level , and therefore dependent on country level data for input .', 'The socioeconomic data , epidemiological data , travel data , and vector suitability data for the principle spreading vectors species are all aggregated to the country level for all countries and territories in the Americas as well as the individual U . S . States .', 'Each variable considered in the model is described in further detail below .', 'All data that we can make publicly available are listed in S1 Data .'], ['The inputs for the GIIM consist of the underlying network structure , attributes of both the nodes and links of the network , and observations on the actual transmission process .', 'In this work the network structure is defined by the passenger air travel movements between regions in the Americas .', 'We denote graph G as G ( V , E ) , where VG is a set containing all the vertices of the graph , while EG contains all the edges of the graph .', 'Edges are denoted as eu , v , where u is the source and v is the destination of a travel route represented by the edge .', 'In this paper , VG contains all countries in the Americas , the French , Dutch , British and American overseas territories , and the individual states of the US , which also defines the spatial resolution of the model .', 'The temporal resolution of the model implemented in this work is at a monthly level , which corresponds to the available travel and suitability data .', 'The edges of the graph exists between a pair of regions if there were passenger air travel movements between them during any month in 2015 .', 'The travel patterns between countries is asymmetric , therefore the resulting graph is directed .', 'We denote this graph as GA .', 'We assign a number of attributes to the vertices and edges of the graph to capture the potential risk factors that may influence the regional spread of Zika virus over time .', 'These attributes correspond to the variables described in the data section .', 'The attributes take the form of normalized real values between zero and one , and include the following: A subset of the attributes are dynamic , i . e . their value changes over time , and therefore are denoted with an additional time index , t .', 'The dynamic attributes include the passenger volumes , the incidence rates in each region , and the vector suitability .', 'The monthly airport travel volumes , V u v t , are aggregated to the state and country level .', 'The mean and standard deviation of the vector suitability for each region for each month is computed as described in the data section .', 'The remaining attributes are static , and are assumed not to vary over the course of the year .', 'The GIIM defines a transmission model on the input graph .', 'Graph-based transmission models require a real value w e t ∈ [ 0 , 1 ] , e ∈ E G A to be present on all edges of the graph , these are called edge transmission probabilities .', 'In this application of the GIIM , the attributes are incorporated into a functional form to represent each time-dependent edge transmission probability .', 'The function takes the form as shown below:', 'w e t = C + α V u v t + β I u t + γ S v t + δ S V v t + ω E v + ρ H v + λ P v ( 1 ) The variables in the function correspond to the set of attributes previously listed , and the coefficients of each attribute are the parameters to be estimated by the model .', 'Values w e t are bounded between 0 and 1 .', 'We will denote the surjective assignment of edge transmission probabilities to the edges as W G A : E G A ↦ [ 0 , 1 ] .', 'In addition to the network attributes , GIIM requires a reference observation of the real-life transmission process it seeks to estimate .', 'In the current application , the observation used is the date of the first reported local Zika cases in each region for the time period considered .', 'The reference point is therefore given as a set of 18 binary vectors; each binary vector corresponds to a month of the observed Zika virus outbreak starting from July 2015 to December 2016 , and assigns a value of 0 or 1 to each node of the graph indicating its transmission state .', 'A value of 1 indicates that the presence of local transmission of Zika virus in the region was reported within or before the corresponding month , and a value 0 indicates that Zika cases have yet to be reported from the region .', 'The GIIM relies on an underlying stochastic simulation to model the spreading process .', 'The compartmental model that is used in this paper is the SI model , which has two states: susceptible ( S ) and infected ( I ) .', 'The graph-based SI infection model is an iterative discrete-time model that assigns states to the nodes of the graph: each node can only be in a single state at any time step , and all nodes must have a state at all times .', 'While GIIM can accommodate a more complex compartmental model , e . g . , SEIR , the SI model is selected to fit the Zika virus application based on the assumption that once Zika virus becomes locally established , that region remains a potential risk of furthering the spread of the virus for the time frame being considered .', 'The reason for allowing the option of non-zero outgoing risk after the reported case count reduced to zero is that there could still be infected individuals in the region , especially given the high rate of asymptomatic cases and reporting error .', 'However , it is important to note that the use of the SI model does not enforce a region to have a positive transmission probability over the entire period modeled , it simply allows a non-zero transmission risk value to be estimated by the model .', 'The actual time-dependent transmission probability is defined as a function of the incidence rate at the origin country among other factors; a probability of zero is a feasible solution of the model , and is actually assigned to many of the links over the course of the outbreak .', 'Given the estimated transmission probabilities , in each step of the simulation , “infected” nodes try to “infect” all their susceptible neighbors according to the transmission probability we connecting them .', 'If the attempt is successful , the neighbor will be infected in the following iterations .', 'If the attempt is unsuccessful , the neighbor remains in a susceptible state , and the infected node can continue to make attempts in the following iterations indefinitely .', 'More formally , the transmission process starts from an initially infected set of nodes A 0 ⊂ V G A at iteration t0 .', 'The rest of the nodes V G A \\ A 0 are susceptible at the beginning of the process .', 'Let A i ⊆ V G A be the set of infected nodes at iteration i .', 'At each iteration , t , each node u ∈ Ai tries to infect each susceptible neighbor v ∈ V G A \\ A i according to the probability w e i , e = ( u , v ) ∈ E G . If the attempt is successful , v becomes infected starting from the following iteration: v ∈ Ai+1 .', 'If more than one node is trying to infect v in the same iteration , the attempts are made independently of each other in an arbitrary order within the same iteration .', 'By definition , the transmission process stops at iteration t if A t = V G A . Since we only simulate a finite portion of the Zika virus epidemic , we stop all transmission models after 18 iterations , corresponding to the observed months of the epidemic at the time of analysis .', 'Within each model run , the transmission process is repeated 10000 times to produce a real value indicating the likelihood of each node being in an infectious states at each iteration , t .', 'The value is calculated by counting the number of repetitions when nodes were in an infectious state , and dividing by the total number of repetitions i .', 'e . 10000 .', 'The GIIM [41] implemented in this work formulates the estimation of edge transmission probabilities as a general optimization task .', 'The model relies on knowledge of the underlying graph and ( at least a subset of ) observations from a transmission process taking place on the network .', 'The real observations take the form o → t ∈ O , where o → is a binary vector and t is a time stamp .', 'Each vector represents a point in time and o → t assigns a binary value to all v ∈ V G A indicating the observed transmission ( or lack there of ) of Zika virus in the region at time t .', 'Set O contains all observations , while set T contains all sample times , i . e . |O| = |T| = 18 .', 'The inputs of GIIM are: an unweighted graph G , a transmission model I , the set of sample times T , and the set of observations O , where O = I n f ( G , W , I , T ) .', 'In this work I is the SI stochastic simulation transmission model defined in the previous subsection , WG: EG ↦ [0 , 1] is the unknown weight assignment , and Inf is a procedure that generates observations at sample times T based on transmission process I taking place on graph G with assigned edge weights we ∈ W , e ∈ E ( G ) .', 'The set of observations , O′ , is a time-dependent vector of real values equal to the probability each node is infected at each timestep , computed from the set of runs .', 'The task of GIIM is to find an estimation W′ of W so that the difference between O and O ′ = I n f ( G , W ′ , I , T ) is minimal .', 'Due to the need to compare a set of binary vectors with a set of real vectors , we compare observations O and O′ using ROC evaluation by pairwise comparing vectors o → i ∈ O and o ′ → i ∈ O ′ for i = 1…18 , computing the AUC value for each pair and averaging over all pairs .', 'The formal definition of the GIIM is as follows: General Inverse Infection Model: Given an unweighted graph G , and transmission model I , the set of sample times T and observations O = I n f ( G , W , I , T ) , we seek the edge transmission probability assignment W′ such that the difference between O and O ′ = I n f ( G , W ′ , I , T ) is minimal .', 'The GIIM defines the estimation of W as an optimization problem , which is solved using an iterative refinement algorithm .', 'The procedure begins with an initial weight configuration W 0 ′ , runs transmission model I , makes observations O′ and computes the error between O and O′ .', 'Based on the error , W′ is refined and the process is repeated , until the error becomes less than an accuracy constant a selected by the user .', 'The search strategy used in this paper is the Particle Swarm Optimization ( PSO ) method [57] .', 'According to the findings in [41] , the method is stable and is able to produce outputs close to the reference , and therefore the solution method chosen for this work as well .', 'It can also be implemented in a parallel environment speeding up computations considerably .', 'Algorithm 1 summarizes the iterative GIIM algorithm .', 'Algorithm 1 Generalized Inverse Infection Model 1: Inputs: G , I , T , O , a 2: Choose initial edge infection probability assignment W′ 3: repeat 4: Compute O ′ = I n f ( G , W ′ , I , T ) 5: Compute d ( O , O′ ) 6: if d ( O , O′ ) ≤a then 7: return W′ 8: else 9: Choose new W′ according to the PSO search strategy .', '10: end if A major modification was necessary in order to adapt the GIIM method to be applied in the context proposed here .', 'The original GIIM method estimates the edge transmission values of the graph directly as real values that are static , i . e . , they do not change over time [41] .', 'In this work the edge weights are given as functions of known attributes on the nodes and edges of the graph , and the task becomes the estimation of these functions , or more specifically , the coefficients of these functions .', 'Several attributes in this application are dynamic , i . e . , they change with time .', 'Thus , it is necessary to further extend the function estimation method to account for dynamic attributes , and to adapt the simulation model to handle dynamic edge transmission values .', 'In this work the edge transmission values are defined using a linear function of known attributes , as defined in eq ( 1 ) .', 'More generally , if a i t ( e ) , e ∈ E G A is the set of attributes , where i represents the i-th attribute and t represents the time period , then the time-dependent edge transmission probabilities w e t are given as w e t = g ( f 1 ( a 1 t ( e ) , c 1 → ) , f 2 ( a 2 t ( e ) , c 2 → ) , … , f ℓ ( a ℓ t ( e ) , c ℓ → ) , c g → ) for all e ∈ E G A , where ℓ is the number of available attributes , f1 , … , fℓ and g are functions and c 1 → , … , c ℓ , c g → → are coefficients of functions f1 , … , fℓ , g .', 'Following the notation proposed in [41] , the functions used to compute the edge transmission probabilities are given as a set of attribute functions f1 , … , fℓ assigned to each invididual attribute , an aggregator function g with the role of creating a single value from the result of the attribute functions and a normalization function ensuring that the result falls between 0 and 1 .', 'This formulation makes implementation of the method easy while retaining the flexibility of the model .', 'Let C denote the set of all coefficient vectors .', 'The values of the attributes can change over time , however the functional form and estimated coefficients are assumed to remain constant over the time period examined .', 'The optimization process of GIIM changes from the estimation of the direct weight assignment W to the estimation of C . This provides a means to identify the key factors contributing to the spread of Zika virus throughout the regions in the Americas .', 'A second advantage is technical; |C|<< |W| , therefore the optimization process is much easier because we are only looking for a limited number of function coefficients as opposed to the edge transmission probabilities for all edges of the graph .', 'For the implementation of the model in this paper , all parameters are bounded between -0 . 5 and 0 . 5 , in order to reduce the solution space for the PSO method .', 'Finally , the resulting edge transmission values are trimmed above 1 and below zero by taking w e t = M A X ( 0 , M I N ( 1 , ∑ i = 1 ℓ f ( a i t ( e ) , c i ) + c g ) ) ) .'], ['The first task of our study is to identify the set of attributes ( and corresponding contribution of each ) to be included in the model .', 'We consider the entire set of attributes previously presented in the data section .', 'A linear weighted sum function as defined in eq ( 1 ) is used to compute transmission probabilities , and the dynamic GIIM method is implemented to estimate the coefficients of the function .', 'Different variable configurations were considered , and the model that produced the best fit was selected .', 'The model fit is based on the quantifiable performance metric , ROC AUC averaged over the entire time period .', 'To evaluate and ensure stability of the proposed estimation method , we ran the algorithm 20 times with the same set of inputs and computed the mean and variance of the estimated model coefficients over all runs .', 'The results of the final model are presented in Fig 5 .', 'w e t = 0 .', '040 + 0 .', '079 V u v t + 0 .', '247 I u t + 0 .', '174 S v t - 0 .', '372 E v + 0 .', '285 P v ( 2 ) The results of the model are highly robust .', 'The estimated coefficients vary minimally across runs , and , more significantly , the ranking of all risk factors remained consistent across all runs ( Fig 5A ) .', 'The expected value of the estimated coefficients represent the relative influence of each attribute in the risk of Zika virus spread between a pair of regions .', 'When interpreting these coefficients it is important to first note that this model is designed to estimate the risk of Zika virus spread between two regions resulting in local , vector-borne transmission .', 'This is different from the risk of Zika infected passenger arrivals .', 'For example , there are multiple locations where travel cases of Zika were continually reported , yet no local cases resulted [27] .', 'The lack of local transmission in these examples could be due to many explanations , including insufficient populations of competent vectors and/or intense surveillance and vector control programs implemented at the destination .', 'Thus , a high number of travel-reported cases does not necessarily translate to a high local transmission risk , and for this reason , the risk of Zika infected passenger arrivals and local transmission risk should be modeled separately .', 'Due to the potential harm posed by local outbreaks of Zika , local transmission risk is the primary focus our analyses .', 'The important distinction between modeling travel-reported cases and local transmission risk is perhaps most evident from the low coefficient estimated for travel volume .', 'In fact , we found infected travelers to be significantly less influential than all the other risk factors .', 'This can be explained by the fact that there is a high level of connectivity between most pairs of regions , and more importantly , the highest volume of air travel exists between and within the U . S . states .', 'Yet , with the exception of Florida [24] and Texas [58] , Zika was not broadly established in the U . S . Thus , we do not identify travel volume to be a driving forces in the spread and transmission of Zika virus in the Americas; travel is a necessary , but not sufficient condition .', 'It is worth noting that a model seeking to estimate the risk of infected passenger arrivals alone would likely find this variable to play much more substantial roles .', 'In contrast , we found that Zika virus spread and local transmission is largely driven by regional attributes at the origin ( incidence rate ) and destination: Ae .', 'aegypti suitability , human population density , and the GDP , with GDP being the most significant ( Fig 5A ) .', 'As expected , a higher incidence rate at the travel origin , which can act as a proxy for the likelihood of an infected individual arriving at the destination , significantly increases the risk posed to the travel destination .', 'Similarly , the results indicate a higher vector suitability at the destination corresponds to an increased risk of transmission .', 'High human population density at the destination is also revealed to increase the risk of transmission , consistent with the required presence of both vectors and hosts for mosquito-borne virus transmission .', 'The health indicator variables were excluded from the final model , as they were not found to have a significant impact .', 'Based on our model results , the most dominant and only negative risk factor is a region’s GDP , i . e . , a higher GDP at the destination corresponds to a lower risk of transmission .', 'Based on the magnitude of the coefficient , the destination’s GDP contributes more than any other risk factor considered .', 'The highly negative coefficient of GDP can be explained by the substantial delay ( or complete lack ) of local transmission in the wealthier U . S . states and certain territories and islands in the Caribbean .', 'GDP is obviously not directly involved in Zika virus transmission , but it may indirectly influence the interactions between components of the cycle: hosts and vectors .', 'Poorer nations likely have lower housing qualities and inhabitants may be exposed to more mosquito bites , e . g . , a lack of screens on windows and doors allowing mosquitoes to enter .', 'They may also have more debris around their homes acting as breeding containers for Ae .', 'aegypti .', 'Lastly , GDP may be a proxy for the available surveillance and vector control resources at the destination , an increase of which would aid in reducing local transmission .', 'Our final model captures the relative contribution of both static and dynamic risk factors to explain the spread and local transmission of Zika virus in the Americas .', 'The AUC ROC for this model averaged over the 18 months is 0 . 923 , which indicates an excellent fit ( Fig 5B ) .', 'For the first month we see perfect classification , since the epidemic was only reported in Brazil , which proves trivial for the estimation method .', 'The second half of 2015 corresponds to a major increase in the number of regions reporting local transmission ( as illustrated in Fig 1 ) .', 'Specifically , between November and December the number of regions reporting transmission nearly doubled from 9 to 16 , and then increased to 32 in January .', 'This proved to be the most challenging part of the estimation process , and the reason for the performance drop below 0 . 9 during the period from October to January .', 'The minimum AUC value of 0 . 83 occurred in November 2015 , which is still considered to be good performance for any classifier .', 'The estimation task gets easier again for the last 9 month characterized by a low but constant rate of spreading between the regions , and performance goes around 0 . 95 again for these months .', 'We can conclude , that even though sudden bursts in the reported local outbreaks decrease prediction accuracy slightly , the method is able to provide accurate estimation .', 'The estimation process took between 3 to 4 hours with the number of iterations between 250 and 350 .', 'A parallel version of the algorithm was implemented in C++ , and the results were computed on a PC with an 4-core i7-7700k 4 , 2 GHz processor .', 'Using the final estimated model , we computed the probability of Zika virus spread between any pair of regions in the Americas resulting in subsequent local transmission ( Fig 6 ) .', 'The link probabilities reveal the highest risk travel routes connecting regions at discrete points in time over the outbreak , as well as how the relative ranking changes over time ( Fig 6A ) .', 'Out of the 2946 feasible edges in the network , only 711 edges have nonzero transmission probabilities , and only 58 of the edges has a value greater than 5% at any point of the observation period .', 'The time-dependent data for the top 100 transmission links , exportation risk , and importation risk are provided in S1 Data .', 'In general , the high risk travel routes are dominated by ones outbound from the Caribbean Islands with the highest incidence rates ( earlier in the outbreak ) , and pointing to the less developed countries and territories of the Caribbean and Central America .', 'These results are corroborated by the early estimated introduction times into countries like Haiti and Honduras relative to Puerto Rico , Mexico , and the U . S . [3 , 4 , 24] , see also www . nextstrain . org/zika .', 'The risk on routes departing a given country , e . g . , Brazil , behave similarly , but vary in magnitude .', 'They also display different behavior than the outgoing risk posed by other high risk countries , e . g . , Martinique .', 'The estimated transmission probabilities fluctuate over time due to changes in the dynamic attributes at both the route origins ( outbreak scale ) and destination ( vector suitability ) , as well as variations in the monthly travel volumes between regions .', 'The effect of these risk factors , for example , the lower Zika incidence rates in Puerto Rico relative to Martinique ( Fig 1B ) , is illustrated by the corresponding temporal differences in transmission risk into Haiti ( Fig 6A ) .', 'The route level risk can be aggregated to provide import and export risk profiles at a regional level .', 'This type of spatial and time-dependent information can help guide policy decisions , such as where to allocate available resources at different stages during an outbreak .', 'The regional level risk is achieved by computing the node strength statistic for all nodes of the network .', 'Node strength is defined as the sum of all weights incident to a node .', 'In the case of a directed network , out-strength , i . e . , the sum of all outgoing link weights , and in-strength , i . e . , the sum of all incoming link weights , are calculated to provide the relative export and import risks .', 'Node strength values can be used to rank the regions according to outgoing ( export , Fig 6B ) and incoming risk ( import , Fig 6C and 6D ) , and more critically , observe how the ranking and magnitudes of the risk change over the course of the outbreak .', 'To determine the regions most likely to contribute to the spread of Zika virus during the epidemic , we estimated the the dynamic exportation risk using the route-level network ( Fig 6B ) .', 'Martinique , Brazil , Colombia , Puerto Rico and Mexico are identified by the model to pose the highest risk of spreading Zika to new regions .', 'Intuitively , the export risk is dominated by the set of counties infected earlier in the outbreak and those with high incidence rates .', 'Martinique stands out as having the highest exportation risk , which peaks during March , corresponding to the month with the highest incidence rate ( Fig 1B ) .', 'The highest exportation risk through 2015 is posed by Brazil and Colombia , which were the two countries reporting early and large outbreaks ( Fig 1A ) .', 'Brazil was identified as the likely source of spread to the first few Caribbean Islands , which is consistent with the phylogenetic data [3 , 4] .', 'Our model estimates that Brazil and Colombia became less prominent in their roles of seeding new Zika virus outbreaks from December , 2015 , to May , 2016 .', 'This time period corresponds to the significant rise in the number of new regions reporting local Zika virus transmission ( Fig 1C ) and the rise of Zika incidence rates in many Caribbean Islands ( Fig 1B ) .', 'The increased exportation risk posed by Martinique during this time captures this behavior ( Fig 6B ) .', 'We similarly aggregated the route-level network at each destination to determine temporal and regional importation risk ( Fig 6C and 6D ) .', 'The regions at highest risk of local transmission are dominated by the less developed countries and territories in Central America such as Belize , and the islands in the Caribbean , such as Haiti , Saint Lucia , Grenada , and Dominica .', 'The high ranking of these regions is due to their low GDP ( Fig 4A ) , high human population density ( Fig 4B ) , and high vector suitability ( Fig 3 ) .', 'For the U . S . , the states with the highest importation risks were Florida , Georgia , and South Carolina , mostly due to their high Ae .', 'aegypti suitability ( Fig 3 ) and incoming travel volume from the affected regions [24] .', 'Compared to much of the Americas , however , these importation risks were low , predominantly due to their high GDP ( Fig 4A ) .', 'In fact , Florida was the only one of those three states ( along with Texas ) that reported local Zika virus transmission .', 'These findings correspond with and reinforce previous route-level risk rankings , that is less developed regions are more likely to see local Zika virus transmission , given they meet the basic requirements for Ae .', 'aegypti-borne virus transmission .', 'Much of the dynamic aspects of our network model are based upon reported Zika virus cases , which are likely biased and vastly underestimated .', 'Moreover , there is often a substantial delay ( 3-12 months ) between actual introduction of the virus and the first reported case [2–4 , 24] .', 'The reporting inaccuracies can be attributed to the high percentage of asymptomatic Zika cases and insufficient surveillance methods , among other factors .', 'While we cannot feasibly correct for all reporting inaccuracies , we conducted sensitivity analyses to account for delays in case reporting ( Fig 7 ) .', 'Both three- and six-months reporting delays were considered , and the model was re-run with corresponding shifts in the data to represent each assumption .', 'While the coefficient rankings slightly changed , likely representing better fits between local vector suitability and Zika incidence rates , the general conclusions were unchanged—low GDP was still the best predictor of local Zika virus transmission .', 'Thus , our results appear to be robust to some reporting inaccuracies .', 'Our work takes a major step towards improving our understanding of the risks associated with Zika virus spread and local transmission; however , there are certain limitations of this analysis that must be noted here and addressed in future research: Our work enhances our understanding of and ability to investigate the risk factors which contributed to the spread and local transmission of Zika virus during the 2015-2016 epidemic in the Americas .', 'For each region , our model is informed by data on regional socioeconomic factors , vector habitat suitability , passenger air travel data , and epidemiological data .', 'We constructed and implemented a dynamic extension of the GIIM to estimate the contribution of each risk factor to the likelihood of Zika virus transmission .', 'Our model relies on a multi-agent based optimization method to estimate the parameters and a data driven stochastic-dynamic epidemic model for evaluation .', 'The GIIM was shown to perform well based on quantitative metrics .', 'Our results from the final model indicate the spread and local transmission of Zika virus was quite multifaceted .', 'As expected , regional attributes influencing vectors ( Ae . aegypti suitability ) , hosts ( human population density ) , and viruses ( Zika incidence rates at origin of travel ) all contributed to the likelihood of establishing local mosquito-borne transmission .', 'Passenger air travel volume , however , was notably less impactful that the other attributes .', 'Therefore , rather than travel restrictions , we predict that mosquito control will be more effective at reducing Zika virus introductions leading to local transmission .', 'This debate recently arose during the 2016 Rio Summer Olympics where some wanted to ban the games to prevent further Zika virus spread [62] .', 'Our results suggest that additional travel for the Olympics was highly unlikely to make a significant impact .', 'From our model , the coefficient most associated with Zika virus transmission was the regional GDP per capita , where a lower GDP corresponded to higher transmission risk .', 'Although GDP does not directly influence transmission , it likely serves as a proxy for mosquito-host interactions [63] and surveillance activities .', 'For example , people living in poverty often do not have the means to protect themselves from host seeking mosquitoes , such as air conditioning and screened windows common in higher income areas .', 'Findings by Netto et al . [64] of higher Zika virus seroprevalence in areas with lower socioeconomic status further support our association .', 'This , now evidence based conclusion that Zika and other Ae .', 'aegypti-borne viruses should be considered diseases of poverty , is also consistent with other expert opinions [37 , 65 , 66] .', 'The two most significant risk factors identified in our work , namely GDP and population density , are often excluded in geographic risk profiling of Aedes vector-borne diseases , and should be considered in future analysis .', 'Our model is not specific for Zika virus and could easily be employed for other mosquito-borne viruses , such as dengue and chikungunya , with sufficient epidemiological and entomological data .', 'Furthermore , the model could be adapted as a tool to inform real-time policy decisions regarding resource allocation for destination-based surveillance and vector control .']]
['Introduction', 'Method', 'Results and discussion']
['An unprecedented Zika virus epidemic occurred in the Americas during 2015-2016 .', 'The size of the epidemic in conjunction with newly recognized health risks associated with the virus attracted significant attention across the research community .', 'Our study complements several recent studies which have mapped epidemiological elements of Zika , by introducing a newly proposed methodology to simultaneously estimate the contribution of various risk factors for geographic spread resulting in local transmission and to compute the risk of spread ( or re-introductions ) between each pair of regions .', 'The focus of our analysis is on the Americas , where the set of regions includes all countries , overseas territories , and the states of the US .', 'We present a novel application of the Generalized Inverse Infection Model ( GIIM ) .', 'The GIIM model uses real observations from the outbreak and seeks to estimate the risk factors driving transmission .', 'The observations are derived from the dates of reported local transmission of Zika virus in each region , the network structure is defined by the passenger air travel movements between all pairs of regions , and the risk factors considered include regional socioeconomic factors , vector habitat suitability , travel volumes , and epidemiological data .', 'The GIIM relies on a multi-agent based optimization method to estimate the parameters , and utilizes a data driven stochastic-dynamic epidemic model for evaluation .', 'As expected , we found that mosquito abundance , incidence rate at the origin region , and human population density are risk factors for Zika virus transmission and spread .', 'Surprisingly , air passenger volume was less impactful , and the most significant factor was ( a negative relationship with ) the regional gross domestic product ( GDP ) per capita .', 'Our model generates country level exportation and importation risk profiles over the course of the epidemic and provides quantitative estimates for the likelihood of introduced Zika virus resulting in local transmission , between all origin-destination travel pairs in the Americas .', 'Our findings indicate that local vector control , rather than travel restrictions , will be more effective at reducing the risks of Zika virus transmission and establishment .', 'Moreover , the inverse relationship between Zika virus transmission and GDP suggests that Zika cases are more likely to occur in regions where people cannot afford to protect themselves from mosquitoes .', 'The modeling framework is not specific for Zika virus , and could easily be employed for other vector-borne pathogens with sufficient epidemiological and entomological data .']
['Since May 2015 , when Zika was first reported in Brazil , the virus has spread to over 60 countries and territories , and imported cases of Zika have been increasingly reported worldwide .', 'However , there is still much uncertainty behind the mechanisms which dictated the rapid emergence of the epidemic .', 'This work introduces a novel modeling framework to improve our understanding of the risk factors which contributed to the geographic spread and local transmission of Zika during the 2015-2016 epidemic in the Americas .', 'The model is informed by data on regional socioeconomic factors , mosquito abundance , travel volumes , and epidemiological data .', 'As expected , our results indicate that increased presence of mosquitoes , human hosts , and viruses increase the risk for mosquito-borne virus transmission .', 'Passenger air travel , however , was less impactful , suggesting that travel restrictions will have minimal impact on controlling similar epidemics .', 'Importantly , we found that a lower regional GDP was the best predictor of Zika virus transmission , suggesting that Zika is primarily a disease of poverty .']
['medicine and health sciences', 'air travel', 'pathology and laboratory medicine', 'viral transmission and infection', 'economic analysis', 'pathogens', 'spatial epidemiology', 'microbiology', 'social sciences', 'geographical locations', 'human mobility', 'viral vectors', 'viruses', 'rna viruses', 'population biology', 'infectious disease control', 'human geography', 'infectious diseases', 'geography', 'south america', 'medical microbiology', 'epidemiology', 'microbial pathogens', 'economics', 'disease vectors', 'brazil', 'people and places', 'population metrics', 'flaviviruses', 'virology', 'viral pathogens', 'earth sciences', 'biology and life sciences', 'species interactions', 'population density', 'organisms', 'zika virus']