Patent Application: US-15839806-A

Abstract:
the present invention relates to a method for predicting outcome and evaluation of clusters . particularly the invention relates to a method of determining deviation and predict future out comes of clusters with certain attributes . in one embodiment , the present invention relates to epidemic outbreaks of disease and , more particularly , to a method for predicting the spread thereof .

Description:
the general description of the invention and how to use the present invention are stated in the brief summary above . this detailed description defines the meaning of the terms used herein and specifically describes embodiments in order for those skilled in the art to practice the invention . the above interests in evaluating clusters are explained and benefits met as can be seen readily from the disclosure which follows and thus met by the present invention . as used herein the term “ points ” refers to individual points or to spatial points . examples of individual points include people , animals , sites , groups or the like having an attribute as part of a whole set . examples of spatial points include mountains , cities , rivers , roads and farms . as used herein “ attributes ” relates to attributes of the points such road accidents , work - related accidents , opinions , social networks , natural resources , weather , computer viruses , crime , epidemics , infections , banking information , internet information and the like . as used herein the term “ spatial coordinates ” refers to any bi - dimensional coordinates including things such as distance , height and weight and the like . distance has its broadest possible meaning . so no only is the measurement of point to point distance included but other abstract distances such as years of service and the like are included . as used herein , the term “ connectivity ” refers to the relationship of attributes between two clusters . in other words , a relationship that tells us potential causes or consequences , for example , why or how did something happen , what could happen later , where or how much has happened and the like . one embodiment of this connectivity is the relationship between clusters of infected individuals and non infected individuals and what would happen over time . i . e . how could the disease spread over time . connectivity can also be used to determine the relative deviation between clusters . so in one embodiment one could look at clusters of individuals and use connectivity to identify a cluster of individuals with a higher rate of disease infection , cancer or the like than other clusters of individuals . as used herein , “ geographic information system ” ( gis ) refers to a collection of spatial features , topographical features or a combination of the two . the gis is collected for a specific geographic area for example for a whole country , for a city county or the like . once a particular geographic area is selected the corresponding gis is collected for that geographic area . as used herein , “ processing the attributes ” refers to sorting , measuring , comparing , ranking the magnitude or like process to correlate the attributes of each point in the set . as used herein “ determining the linkage ” refers to determining the number of links per individual or spatial point , the index of each link per individual or spatial point , time the attribute was reported , or combinations of these or the like ; the following embodiment of an epidemic spread further illustrates the invention and teaches one skilled in the art how the invention , works , is applied and calculated . presented in one embodiment to test the influence of spatial connectivity on disease dispersal during an epidemic , geographically referenced epidemic data are needed . the 2001 epidemic of fmd in uruguay offers an opportunity to evaluate diffusion over time and space during an epidemic . cattle were predominantly infected in a country previously free of fmd . 23 - 25 the minimal replication cycle of fmd virus is estimated to be 3 days . 26 studies 27 - 29 on fmd and other diseases have indicated heterogeneous spatial spread and used the centroids of irregular polygons ( i . e ., counties ) as units of analysis . road networks may influence dispersal of fmd virus . 24 , 25 , 30 3 objectives are met by the present invention : a determination is made to detect whether infected sites are spatially or temporally auto - correlated ; if sites are clustered , to measure the contribution of each spatial link to the overall spatial - temporal autocorrelation ; and that information is used to generate and evaluate hypotheses on the various potentials for disease spread during an epidemic for specific counties . details of this epidemic have been reported 23 - 25 elsewhere . initial cases of fmd were identified in the southwestern quadrant of uruguay , a non - urban , cattle - raising region characterized by higher road density than the national median ( fig1 a - 1b and 2 a - 2 d ). several interventions were implemented over time , including a nationwide ban on animal movement ( implemented on day 2 of the epidemic ) and a nationwide program of vaccination . however , human traffic was not interrupted . milk trucks continued to visit dairy farms and collect milk throughout the duration of the epidemic . in addition , no vaccines were available in the country at the time the epidemic began . 31 , 32 although a decision to acquire & gt ; 10 million doses of vaccine was made within a week after the onset of the epidemic , no data were available in relation to where or when the first vaccination was implemented . it is estimated that at least 3 days are required for immunologically naive animals to synthesize antibodies after vaccination with a high - potency vaccine . 33 no spatial - temporal data were available as to whether vaccine - induced antibodies reached protective titers . a second vaccination was implemented later . two gis packages a , b were used to geographically reference data and create maps . an official map of uruguay , c including the location and area of the 276 counties , was used . on the basis of the 2000 agricultural census for uruguay , 248 counties ( cattle - raising regions ) were selected . of those , 163 counties contained infected animals at some time during the 11 - week period that began on apr . 23 , 2001 . geographically coded data on weekly ( county level ) and daily ( for the first 6 days only ; farm level ) number of cases were retrieved from public sources and processed as described elsewhere . 24 , 34 - 37 four steps were used to determine the intercounty centroid distance . first , the x - and y - coordinates for each county &# 39 ; s surface were identified by accessing the x - and y - values in the shape field . second , the center value for each polygon ( centroid ) was provided by use of the gis packages . third , a point layer was generated from the x - and y - values of the centroid for each county . fourth , distances between all centroids were calculated by use of the gis tools , which selected a distance larger than the largest distance between any pair of points in the territory under study . three steps were used to generate data on road density . first , the total area of each county was determined by accessing the county value for area . second , the national highway layer ( excluding urban areas ) c was intersected with the county layer to characterize and identify road segments by county . length of road segments was then summarized for each county ( i . e ., the total length of roads was divided by total area of the county ). the gis - generated matrix of all pairs of intercounty ( centroid - to - centroid ) distances ( 13 , 203 county pairs ), the table containing density of county roads , and the matrix including the number of infected cattle per week and county identifier were transferred into and processed by use of technical computing software . spatial connectivity involved euclidean distances ( i . e ., number of kilometers ) between counties with infected cattle ( distance between centroids ) and road density ( road distance divided by county area , a non - euclidean distance measure ). the moran i coefficient was used to analyze spatial autocorrelation . 13 positive values for spatial autocorrelation indicate that sites spatially closer to each other than the mean distance have similar numbers of cases , whereas negative values for spatial autocorrelation indicate the opposite . the moran i coefficient of autocorrelation was calculated as follows : where n is the number of counties , i and j are counties ( i and j cannot be the same county ), w ij is the spatial connectivity matrix , z i is the difference between the prevalence in county i and the overall mean prevalence , z j is the difference between the prevalence in county j and the overall mean prevalence , s 0 is an adjustment constant , k is a county index , and z k is the difference between the county index and overall index . in addition , z i = x i − x , where x i is the weekly number of cases / 100 farms in county i and x is the mean prevalence . the value for w ij is calculated by use of the following equation : w ij = f ( d ij , r i , r j )=( d ij ) − a ( r i r j ) b eq . 2 where d ij is the matrix of the euclidean distance between counties i and j ( i and j cannot be the same county ), r i is the road density for county i , r j is the road density for county j , the value for variable a is a measure of the degree of epidemic diffusion in relation to distance ( i . e ., there is greater diffusion at shorter distances ), 37 - 41 and the value for variable b is a measure of the extent of connectivity between counties ( i . e ., greater road density results in greater connectivity ), regardless of distance . for fixed positive values of variable a , large values of variable b support local spread as well as long - distance spread because higher local road density is associated with higher interstate highway density . values for variables a and b were estimated by maximizing the spatial autocorrelation coefficient as reported elsewhere6 as follows : where a & gt ; 0 , b & gt ; 0 , and t is time ( week of the epidemic ). the value for s 0 was calculated as follows : interactions of space and time were analyzed by use of the mantel coefficient i s - t . 14 , 15 . the i s - t coefficient was calculated by use of the following equation : where y ij indicates the closeness in time between infections and i and j cannot be the same county . the first moments of the moran i and mantel i s - t statistics are reported elsewhere . 6 observations were assumed to be random independent samples from an unknown distribution function relative to the set of all possible values of i or i s - t when the x i were randomly permuted around the county system . 6 the matrix y ij was defined as y ij = 1 when county i had values greater than the mean number of cases / 100 farms ( total number of susceptible farms / county ) at week t and county j also had values greater than the mean number of cases / 100 farms at week t − m ; otherwise , y ij was equal to 0 . this cross - correlation at lag m measured the temporal correlation of events at time t and those at a specified preceding point ( i . e ., m weeks earlier ). interaction between county pairs was measured as a function of their distance from each other as described elsewhere . 6 the graphic display of the global spatial autocorrelation coefficient ( moran i ) plotted against the distance lag ( correlogram ) was determined by use of the following equation : where g is the distance between the 2 counties , the matrix w ij contains values of 1 for all the links among county pairs ( i , j ) located within the distance g and values of 0 for all other links not included within the euclidean distance g , and i and j are not the same county . the temporal correlogram is the plot of i s - t as a function of the time lag m . hence , the temporal correlogram was used to determine the extent of spatial - temporal autocorrelation for various time lags . on the basis of network analysis , relationships between nodes ( i . e ., counties ) can be described by their links . 5 , 7 county pairs were considered connected by a spatial link when their contribution to the global spatial autocorrelation coefficient did not equal 0 . the contribution of specific spatial links was defined as the link strength ( index ) between counties with infected cattle ( i , j ) located within a distance g , as indicated by use of the following equation : where i ij ( g ) is the contribution of the specific spatial link . spatial - temporal autocorrelation and link indices were calculated by use of mathematical software . d normality ( no . of farms / county and link index , which were tested by use of the anderson - darling test ) and comparisons among medians ( assessed by use of the mann - whitney test ) were conducted by use of a statistical program . e for all tests , values of p & lt ; 0 . 05 were considered significant . the 2001 epidemic began in the southwest portion of uruguay and reached a peak ( county - level ) farm prevalence at week 5 ( table 1 ). the median road density of all counties reporting infected animals during the first week was 0 . 24 km / km2 , which differed significantly ( p = 0 . 01 ) from that for the remainder of the country ( 0 . 12 km / km2 ; fig1 ). a dissimilar spatial pattern was observed over time ( fig2 a - 2d ; table 2 ). the distribution of the number of susceptible farms per county did not disprove a normal distribution ( p & gt ; 0 . 05 ; fig3 a - 3b ). the normality assumption of the spatial autocorrelation ( which requires an estimated minimum of 20 county pairs / observation ) was met during at least the first 9 weeks of the epidemic because all distance lags up to approximately 440 km reported & gt ; 20 county pairs . maximization of the spatial autocorrelation index was evident when variable a = 0 . 46 and variable b = 0 . 06 ( data not shown ). the moran i null hypothesis ( lack of spatial autocorrelation ) was rejected . until at least the sixth week of the epidemic , sites closer to each other ( clusters ) had significantly more infected cattle than sites located at the mean ( or greater ) distance from each other ( fig4 a - 4b ). in addition , analysis of the mantel i s - t indicated that in weeks 1 through 6 , spatial clusters were associated with time because adjacent sites had significantly more infected cattle at shorter time periods than sites more distant in time and place . because exotic diseases have zero prevalence before an outbreak and every infection needs to be controlled ( regardless of the size of the susceptible population ), mantel and moran tests were also calculated without considering the total size of the susceptible population , and both calculations yielded similar results . analysis of spatial correlograms ( conducted before and after vaccination was implemented ) indicated a significant positive autocorrelation among county pairs with infected animals located within approximately 120 km from each other for weeks 1 and 2 of the outbreak and within 80 km of each other for weeks 3 through 11 . a significant negative spatial autocorrelation was observed for county pairs with infected cattle located 120 to 400 km from each other only at weeks 1 and 2 of the outbreak . a second cluster , which was not significant , was evident for county pairs with infected cattle located & gt ; 400 km from each other ( fig5 a - 5c ). the temporal correlogram indicated significant temporal - spatial autocorrelation for time lags of up to 3 weeks ( m & lt ; 4 ). when specific weeks were considered , spatial correlograms did not reveal regional effects . during the first 6 weeks of the epidemic , significant positive spatial autocorrelation was observed each week for county pairs with infected cattle located within 120 km of each other , whereas a significant negative autocorrelation lasted for at least the first 5 weeks ( fig6 a - 6b ). analysis of infective link indices ( percentage of the overall spatial autocorrelation explained by specific infective links ) revealed a clear departure from normality ( fig7 a - 9c ). county pairs with infected cattle located & lt ; 120 km from each other during weeks 1 and 2 had 10 links ( including 5 different counties ) with indices substantially higher than the mean . three of those 5 counties also had the highest link indices at weeks 3 through 11 . the remaining 2 counties were involved in significant long - distance links for weeks 1 and 2 , and analysis also suggested that they departed from normality , but not significantly , for weeks 3 through 11 ( table 2 ). * percentage of the overall spatial autocorrelation index explained by a specified spatial infective link index connecting 2 counties it is assumed to be the infector and the other is assumed to be the target . † counties with ≧ 2 links ( both of which had high indices ) are regarded to possess greater potential for epidemic spread ( infector site ), whereas those observed with only 1 link or observed at a later time during the epidemic are regarded as target sites . ‡ represents weeks 1 and 2 during the epidemic for 2 . 306 spatial links with a mean ± sd link index of 0 . 043 ± 0 . 15 . § represents weeks 3 through 11 during the epidemic for 2 , 151 spatial links with a mean ± sd link index of 0 . 046 ± 0 . 14 . ∥ county no . 1705 did not appear to have links by itself because all 3 links to it are explained by links for counties nos . 1704 , 1707 , and 1709 . ¶ represents weeks 1 and 2 during the epidemic for 394 spatial links with a mean ± sd link index of 0 . 254 ± 0 . 23 . # because counties nos . 407 and 409 already contained infected cattle at week 1 and county no . 105 did not report infected cattle until week 5 , these connections appear to rule out county no . 105 as the site that infected counties nos . 407 and 409 . analysis of the data suggested 3 classes of counties in terms of potential disease dispersal during the epidemic . the first class included 5 counties in which infected cattle were observed within the first 3 days of the epidemic ( minimal time compatible with a replication cycle of the infective agent ; hence , possible primary cases ; fig7 a - 7b ). all of these counties , except for 1 , had low index links . the second class included 5 counties that had the highest index links connecting with ≧ 2 other counties . one of the counties was possibly a primary site ( with infected animals reported within 3 days of the outbreak ), whereas the other 4 counties all reported infected cattle within 4 to 6 days of the epidemic . these counties had both short - and long - distance connections . the third class involved counties reporting infections after week 1 of the epidemic and had mean link indices ( counties regarded as targets ). when 2 counties were connected , time during the epidemic helped to generate hypotheses that distinguished the putative infector ( earlier case ) from the putative infected ( later case [ target ]; fig9 a - 9c ; table 2 ). when 1 county of the pair connected by a high index link was involved in multiple links , but the other county was not , the first county was hypothesized to be the infector ( table 3 ). * counties with a high index link ( sufficient counties ) are those that have substantially high infective connectivity indices ( at last 3 . 5 times greater than 2 sds ), link with at least 2 other counties , and report infected cattle earlier than the other county sharing the infective link . † counties without a high index link ( necessary counties ) are those that report infected cattle during the first 3 days of the epidemic ( minimal time for the replication cycle of fmd virus ) and hence are hypothesized to be primary cases and also have link indices within the mean + 2 sds . ‡ county no . 1707 is a county with a high index link that reported infected cattle during the first 3 days of the epidemic ( primary cases ). § expressed in percentages , counties with a high index link reported & gt ; 2 times as many cases ( 332 / 160 [ 207 . 5 %]) as counties without a high index link . expressed as area , total surface for counties with a high index link represented almost half that for counties without a high index link ( 3 , 737 . 8 km 2 / 7 , 000 . 0 km 2 [ 58 . 4 %]). expressed as total number of cases prevented per km 2 , a control campaign implemented in counties with a high index link could have prevented 3 . 5 times more cases per square kilometer than a similar campaign implemented in counties without a high index link ( 0 . 478 / 0 . 138 = 3 . 51 ). ∥ expressed as median number of cases prevented per county , a control campaign implemented in counties with a high index link could have prevented 0 . 073 cases / km 2 , which was significantly ( p = 0 . 02 mann - whitney test ) higher than the number of cases prevented per county ( 0 . 027 cases / km 2 ) had the same control campaign been implemented in counties without a high index link . all counties reporting primary cases did not appear to facilitate spread of the disease during the epidemic . four of 5 counties that had the highest link indices and connected with at least 2 other counties had 2 . 5 times as many cases by week 11 as 4 of 5 counties that contained cattle infected during days 1 to 3 of the epidemic . the second group of counties ( counties with a high index link ) reported their first infected animal on days 4 to 6 of the epidemic ( time frame compatible with a secondary infection ); which combined with another high index link county that reported an infected animal at day 1 to 3 , this provided a county median of 0 . 073 cases / km 2 by week 11 , whereas the remaining counties reporting cases at days 1 to 3 ( none of which were high index link counties ) had significantly ( p = 0 . 02 ; mann - whitney test ) fewer infected cattle ( county median , 0 . 027 cases / km 2 ) by week 11 ( table 3 ). counties with a high index link ( n = 5 ) also had a significantly ( p = 0 . 01 ) higher median road density ( 0 . 26 km / km 2 ), compared with the 271 other counties with infected cattle ( 0 . 126 km / km 2 ). because observational epidemiologic analyses do not allow experimental designs , theories can only use historical data to attempt validation . however , such data may possess unknown sources of bias or lack critical variables . for example , the number of farms considered in the study reported here was based on the 2000 agricultural census , a data set not necessarily applicable for the study of this epidemic . accordingly , the model described should not be perceived as an analysis of the fmd epidemic that took place in uruguay in 2001 but , instead , as an evaluation of a spatial method that uses a hypothetical ( although realistic ) scenario for the epidemic . despite that caveat , the analysis of assumptions on which spatial autocorrelation was based revealed adequate sample size (& gt ; 20 county pairs / observation ) and no departure from normality . 29 two measures of spatial - temporal autocorrelation ( with and without consideration of denominator data ) yielded similar results . similar week - specific correlograms suggested that delayed reporting did not bias these findings . the use of euclidean and non - euclidean distances was justified by the fact that there was a maximized spatial autocorrelation index when variable a = 0 . 46 and variable b = 0 . 06 . 6 significant positive (& lt ; 120 km between counties with infected animals ) and negative (& gt ; 120 but & lt ; 400 km between counties with infected animals ) spatial autocorrelations were observed every week for at least the first 5 weeks ( fig6 a - 6b ). such findings suggested that , once structured , the epidemic network was rather robust and static . three major spatial autocorrelation patterns have been described42 : a monotonic decreasing pattern ( a positive - only significant autocorrelation without a significant negative autocorrelation ; also known as a patchy pattern ); a bimodal pattern characterized by significant positive spatial autocorrelation for short - distance lags , followed by significant negative spatial autocorrelation for long - distance lags , as was evident in the study reported here ; and lack of spatial patterns ( when the moran i coefficient is not significant ). although monotonic and decreasing moran indices ( e . g ., lacking a significant negative autocorrelation ) are usually found in other fields , negative structures are not rare in epidemiologic investigations . 29 possible causes of significant negative autocorrelations include poor local connectivity for 1 member of county pairs ( e . g ., lower road density , factor associated with lower farm density , or fewer adjacent farms ). 24 , 25 a correlogram pattern with significant positive and negative autocorrelations for short - and long - distance lags , respectively , can be interpreted as a linear gradient at macroscales such that when 1 member of the pair is situated farther than a certain critical distance from the other member of the pair , case prevalence typically has opposite values . 42 nonsignificant links at even greater distances for lags (& gt ; 400 km ) resembled small - world - like connections . 5 as indicated by the lack of significance , such connections do not necessarily result in additional disease spread during an epidemic because local conditions ( i . e ., poorer local connectivity ) may prevent viral dispersal spatial analysis facilitated data - driven generation of hypotheses . counties with infected cattle could be categorized as possessing greater potential for disease dispersal during the epidemic on the basis of 3 criteria ( having a high index link [ i . e ., to be an outlier or county with a high index link ], connecting with ≧ 2 other counties , and reporting infections before the other member of the pair ). counties reporting infections on days 1 to 3 of the outbreak ( primary cases ) were regarded as necessary sites , whereas those displaying higher index links ( and connecting with at least 2 additional counties ) were hypothesized to possess greater risk for other counties ( sufficient cause of disease spread during the epidemic ). counties paired with those that had sufficient cause of disease spread were suspected to be target sites . this working hypothesis distinguished counties infected first ( necessary causes , although not necessarily the cause of disease spread ) from those that had a high index link ( i . e ., those hypothesized to seed new cases into target sites ), regardless of when and where they got the infection . this conceptualization is similar to that of a model in which it was proposed that spatial features result in differing diffusion models during an epidemic . 40 although daily data on time of detection of infected animals facilitate the richest generation of hypotheses , even when such data are not available or are available but not used because of possible errors ( e . g ., delayed reporting and underreporting ), information on link indices alone identifies county pairs that have indices much higher than the mean ( outliers suspected to influence disease dispersal ). although other factors associated with disease spread during an epidemic ( i . e ., markets ) cannot be ruled out , spatial analysis may generate evidence of case clustering , whether there are short - or long - distance connections ( or both ), and whether there are changes in location of cases over time in relation to interventions . identification of infected sites with greater epidemic risk ( counties with a high index link ) did not support the hypothesis that all infected cattle had equal influence on disease spread nor the theory of homogeneous mixing , which assumes that all susceptible and infected cattle are located at similar distances from each other and possess similar risk for becoming infected or for infecting others . 40 this theory results in undifferentiated control policies , such as implementation of buffer rings ( i . e ., regional circles of fixed diameter within which the same control policy is conducted ). 43 the fact that the first county with infected cattle and 3 other counties in which there were primary infections apparently failed to promote disease spread also argued against the homogeneous mixing theory . spatially explicit assessment of infective connectivity may be applied to evaluate control policy . for example , when only 2 time periods were considered , spatial autocorrelation analysis revealed a reduction of approximately 40 km in the mean distance between counties for the cluster ( from 120 km at weeks 1 and 2 to 80 km at weeks 3 through 11 ), which supports the hypothesis that vaccination reduced disease spread during the epidemic . however , evaluation of week - specific correlograms did not reveal evidence of regional differences up to week 6 of the epidemic , which suggests that the 40 - km reduction may reflect the end of the epidemic ( when many counties did not report cases ). these results may support the hypothesis that the conclusion of the epidemic was attributable to several factors , including lack of susceptible herds and a ban on animal movement that was imposed in week 1 . the approach described here was also informative , facilitating the explanation of apparent contradictions . although a second cluster was suggested by correlograms for sites located at & gt ; 400 km between counties with infected cattle before and after vaccination was conducted , which is in agreement with the expected limited disease dispersal for infected animals located at the edge of the territory being infected , 40 the cluster at & gt ; 400 km was not significant ( fig5 a - 5c , 6 a - 6 b , and 9 a - 9 c ). however , at weeks 1 and 2 , link analysis identified 2 counties that had a high index and long - distance connections . the contradiction between ( global ) correlogram analysis and link analysis may be explained once local factors are considered ( i . e ., edge effects and a lower density of local roads in target counties connected by long - distance links may prevent further disease dispersal because there is poor local connectivity ). cost - benefit analysis may also be generated by the approach used in the study reported here . had a policy focusing on all counties reporting primary cases been adopted ( on the basis of the theory that all cases equally contribute to disease spread during an epidemic ), it may have been inefficient and insufficient . in contrast , a policy focused on high - index link counties could have been 2 . 5 to 3 times more beneficial than undifferentiated control policies ( table 3 ). observations of significant case clustering and significant negative autocorrelation ( for counties located & gt ; 120 to & lt ; 400 km between counties with infected cattle ), noticed as early as week 2 ( when vaccination had not been implemented ), could have led to differentiated control measures ( i . e ., regionalization ). 44 infective link analysis can be interpreted by considering epidemics as processes that connect at least 2 points through a line . the local moran test has been used 12 , 45 , 46 to focus on the contribution of each point to the overall ( global ) spatial autocorrelation . in contrast , the method described here focused on the line connecting the 2 points . although local moran tests assess inputs and outputs , infective connectivity emphasizes the intermediate process that takes place at some time point before the outcome is noticed . such emphasis informs on earlier phenomena , which can be used to generate hypotheses on factors facilitating ( or preventing ) disease dispersal during an epidemic and possibly to identify case clustering in adjacent sites and in sites located far apart from each other . when based on data of a smaller scale ( i . e ., farm - level data ), spatial autocorrelation and link analysis may facilitate real - time control of rapidly disseminated diseases . based on the above example the inventors have expanded the invention and the following information will aid in further calculations . a procedure aimed at monitoring attribute patterns over space and / or time such that it generates non - overlapping diagnostic hypotheses . monitoring is based on , at least : 4 ) the identifier corresponding to each individual ( e . g ., a cow ), and 5 ) the identifier corresponding to each attribute ( e . g ., a bacterial strain ) corresponding to each individual and date . based on data described above , the following indicators are then created : 1 ) the intrapoint or interpoint ( e . g ., interfarm or intrafarm ) attribute ratio or inter - p ar / intra - p ar ( the number of individual attributes [ e . g ., one bacterial strain ] expressed as percentage of all attributes at a given spatial point / date , 2 ) the attribute spatial spread or a - distnc ( the distance assumed to be traveled by a given attribute , as calculated from the interfarm distance matrix , expressed in km or miles ), 3 ) the attribute spread velocity or a - speed ( distance traveled by an individual attribute / time , e . g ., km / year ), and 4 ) the product of the interfarm attribute ratio times the attribute spread velocity ( intra - p ar times a - speed ), or attribute geo - temporal spread index ( a - gtsi ), which may be expressed with and without adjustment for the average number of spatial points where a given attribute has been recorded per individual attribute / per unit of time . 1 ) hypothesize disease as due to “ non - local ” factors ( i . e ., due to specific a &# 39 ; s ), when greater than average a - gtsi are observed , 2 ) hypothesize disease as due to “ local , environmental ” factors ( e . g ., individual farms ), when higher than average intra - p ar and / or lower than average a - speed were generated ) are observed , and 3 ) hypothesize disease as due to “ local , individual ” factors ( e . g ., cow - related ), when low intra - p ar and / or low a - speed are observed . a procedure aimed at detecting aggregations of individuals displaying greater / lower than average values of some attribute than those of the population at large ( clusters ) which may or may not possess high / low influence in the dissemination of that attribute within the population at large ( with a high / low degree of connectivity ). 1 ) the spatial location of the cluster ( composed of , at least , 2 “ points ” [ e . g ., cities ]), and 1 ) the spatial location of each point ( e . g ., a city &# 39 ; s coordinates ), 2 ) the inter - point distance ( whether euclidean or non - euclidean ), 3 ) the magnitude of the attribute of interest at each point ( e . g ., the prevalence or percent of children infected with the flu virus at a given school ), 4 ) the number of links per spatial point ( with the attribute ), 5 ) the link index ( the “ weight ” or “ width ” of each link ), and 6 ) ( if available ) the time the attribute has been reported . a procedure aimed at estimating the connectivity of a point pertaining to a network . connectivity analysis is based on 2 ( or 3 ) factors : 2 ) the link index ( the “ weight ” or “ width ” of each link ), and 3 ( if available ) the time the attribute has been reported . alone or combined , these factors can be used to identify and / or rank individual clusters . the number of links and the link index are defined . alone or combined , these factors can be used to estimate the connectivity ( expressed as a rank or degree ) in relation to the network that point is associated to . a procedure aimed at informing decisions based on cost - benefit like analyses that uses cluster detection and / or cluster connectivity data . the population at large , upon which more beneficial / less costly decisions are to be made , is identified by a variety of procedures , including : 1 ) determination of the average cluster size ( diameter , expressed in kilometers or miles ), based on inter - point euclidean distances ( as reported in the attached example , by using ripley &# 39 ; s k function ), 2 ) determination of the actual cluster size , 3 ) determination of the number of individuals located at each point , by using georeferenced data , 4 ) comparison of benefits and / or costs , expressed as ratios between the susceptible population ( potential benefits or protected individuals ) and the intervened population ( that on which there is knowledge on some attribute , as measured above ), in any of these forms : a ) higher number of benefited / protected cases on per square kilometer basis per each intervened square kilometer , b ) larger ratio of protected / benefited units ( individuals , spatial points ) per intervened unit ( individuals , spatial points ), as here described , c ) smaller territory / fewer spatial points to be intervened per benefit unit , as here described , d ) optimal number of benefits ( e . g ., protected individuals ) per cost unit ( e . g ., intervented individuals , intervened spatial points ) as determined by roc analysis and based on georeferenced data ( as here described ). since other modifications and changes varied to fit particular operating requirements and environments will be apparent to those skilled in the art , this invention is not considered limited to the example chosen for purposes of this disclosure , and covers all changes and modifications which does not constitute departures from the true spirit and scope of this invention . having thus described the invention , what is desired to be protected by letters patent is presented in the subsequently appended claims . 1 . rainham d g c . ecological complexity and west nile virus - perspectives on improving public health response . can jpublic health 2005 ; 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