Snow's case revisited: New tool in geographic profiling of epidemiology

braz j infect dis 2 0 1 7;21(1):112–115

w w w . e l s e v ie r . c o m / l o c a t e / b j i d

The

Brazilian

Journal

of

INFECTIOUS

DISEASES

Brief

communication

Snow’s

case

revisited:

new

tool

in

geographic

profiling

of

epidemiology

Alessio

Papini

,

Ugo

Santosuosso

a_{UniversityofFlorence,DepartmentofBiology,Firenze,Italy}

b_{UniversityofFlorence,DepartmentofClinicalandExperimentalMedicine,Firenze,Italy}

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Articlehistory: Received27July2016 Accepted30September2016 Availableonline9November2016 Keywords: Geographicprofiling Geographicepidemiology Cholera JohnSnow

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GeographicProfilingtechniqueisusedtofindtheoriginofaseriesofcrimes.Themethod wasrecentlyextendedtootherfields.Oneofthebestrenowneddatainepidemiologyisthat byJohnSnowduringanoutburstofcholerainLondon.WewrotePythonscriptstoperform theanalysestoapplytheGeographicProfilingforindividuatingthestartingoriginofan infectionbyusingtheoldSnow’sdataset.Wemodifiedthemethodbyapplyingaweightto eachpointofthemapwherecasesofcholerawerereported.Theweightwasproportional tothenumberofcasesinagivenlocation.

ThismodificationoftheGeographicProfilingmethodallowedtoindividuateinthemap anareaofmaximumprobabilityoftheinfectionsource,whichwasafewmeterswideand includingthehistoricallyknownsourceofcholera,thatisthe“classical”waterpumpat BroadStreet.

Themethodappearstobeausefulcomplementinordertoindividuatethesourceof epidemicswhenavailabledataaboutthecasesoftheinfectionscanbesummarizedona map.

©2016SociedadeBrasileiradeInfectologia.PublishedbyElsevierEditoraLtda.Thisisan openaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/ by-nc-nd/4.0/).

Introduction

GeographicProfiling(GP) isananalytictoolwidelyused in criminologyinordertoidentifyonamap anarea of high-estprobabilityassumedtocontaintheoriginoflinkedevents, typicallycrimesexecutedbyaserialoffender.1_Themethod

wasextendedfromcriminologytootherfieldswhereitwas possibletoidentifyaseriesoflinkedeventswhichmighthave

∗ _{Correspondingauthor.}

E-mailaddress:[email protected](A.Papini).

originated from a starting point in the space (represented onatwodimensionalmap).Fieldsofapplicationotherthan criminologyhavebeen:invasionbyalienspecies,2–5

bumble-bees foraging and nest location,6,7 _{and infectious diseases}

targeting.8,9

GP usesthecoordinatesonthemappedevents,creating aprobabilitysurface,theso-calledgeoprofile.1_{Thegeoprofile}

does notindicatetheexact origin ofthe events,but rather prioritizeaseriesofgeographicalpoints,basedonthedata.1

http://dx.doi.org/10.1016/j.bjid.2016.09.010

1413-8670/©2016SociedadeBrasileiradeInfectologia.PublishedbyElsevierEditoraLtda.ThisisanopenaccessarticleundertheCC BY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/4.0/).

brazj infect dis.2017;21(1):112–115

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Thegeoprofilewillprovideonthemapadecreasingprobability densityoffindingthesourceoftheeventsdrawnonthemap.1

Themodeldoesnotsearchsimplythegeographical cen-terofthe events,but instead it considersadistance-decay function,suchthattheprobabilityofaneventwillbelower byincreasingthe distancefromthe centeroforigin;and a bufferzone,withinwhichtheprobabilityofanevent tends tozero.1_{Thedistance-decayfunctionisrelatedto}

maximiz-ingparsimonyinmovement,ineconomicalandenergyterms. Surprisingly,thesefunctionsrevealedtobefoundnotonlyfor humans(criminals),butalsoevenforinvasive(nothuman) species2,3_{andinfectiousdiseases.}8–10

Theneedforanalyticaltoolstorecognizethesourceofthe spreadingof“something”(generallyathreat)hasalwaysbeen animportanttask.11_{Oneofthebestknowncasesis,in}

epi-demiology,thatofcholeraoutbreakinLondon,1854,studied byJohnSnow12_{andwidelycitedasaseminalworkinspatial}

epidemiology13_{[13andreferencestherein].Dr.Snowtagged}

thecholeracasesandthewaterpumpsonthemapof Lon-donandsearchedforthearea withthehighestnumber of cases,sodiscoveringthattheoriginoftheoutbreak(the so-calledfocus ofinfection) wasa contaminated waterpump inBroadStreet.ThetaggedcholeracasesdrawnbySnowon themap ofLondon canbeconvertedinadatasetof coor-dinates,thatwasalreadyusedbyLeComberet al.8 _totest

theGPmethodfortargetinginfectiousdiseases.LeComber etal.8_{wereabletomarkarestrictedareainthemapof}

Lon-doncontainingthefamouswaterpumpofBroadStreet(see Fig.1CandDintheirarticle).Theseauthorsusedasinputdata theindividualaddresseswherecaseofdeathsduetocholera hadoccurred,thatis321addresses,whilethetotalnumber ofcasesamountedto575,sincemorethanonecasemight haveoccurredatthesameaddress.LeComberet al.8_used

thisapproach“toavoidthepossibleproblemofspatial tempo-ralnon-independenceduetosecondaryinfectionsatagiven address”.Ourapproachincluded,instead,allcasesassigning aweighttoeachpoint(addresses)proportionaltothenumber ofcases.Weoverlookedpossiblesecondaryhuman-to-human contagions, since cholera should not easily transmit from person-to-person,whileitstransmissionisknowntobemore food-orwater-born.14 _{Forthisreason,weinterpretedmore}

thanonecaseinthesameaddressasindependenteventsand hencesummable.

Therefore,hereweproposeanewmethodofapplyingGP inwhichadifferentweightisassignedtoeachpointofthe mapproportionallytothenumberofcasesoccurredineach point.

Methods

The data about the positions of cases on the map were acquiredwith Neuronmorpho(http://www.southampton.ac. uk/∼dales/morpho/),apluginofImageJ(NationalInstituteof Health;http://rsb.info.nih.gov/ij/),thatcanreadamap posi-tion with amouse click, building a csv filecontaining the coordinatespointbypoint.Weightswereaddedmanually.Our methodcalculatestheGPbyweightingeachpointofthemap indirectproportionalitywiththenumberofcasesoccurredin agivenpointofthemap.Thatis,somepointsofthemapare

moreimportantthanothers.Thedatawereanalyzedwitha Pythonscript(Geoprof3.0.2.py).

CrucialfortheGPanalysisistheassignmentofthevalues B,correspondingtotheradiusofthebufferzone.2_Inour

anal-ysisweusedB=30,correspondingtoabufferzoneof30pixels (about15monourmap),thatisquitesmall,withrespectto other GPanalysesinotherfields,suchasthose onmalaria casesinCairo.9_{WeevaluatedmoreBvalues,calculatingthe}

impactontheanalysis.TheGPtechniqueisdescribedindetail inPapinietal.3_{ThevariableB(thebufferzone)isofcourse}

dependentonthemapmagnificationandonthemap resolu-tion,sinceBisexpressedinpixels,whiletheactualmeaningof thebufferzonecanbeunderstoodonlyifexpressedinmeters orkm.

The Python scripts were written by the authors and can be retrieved from the site www.unifi.it/caryologia/ PapiniPrograms.html.ThescriptswereexecutedwithPython 2.7.3 (http://www.python.org/), running in Ubuntu 12.04 LTSoperatingsystem, kernel2.6.32.ThePython(>=2.6 ver-sion)programsneedNumPy(http://www.numpy.org/),SciPy (http://www.scipy.org/), Matplotlib (http://matplotlib.org/), Scikit-learn (http://scikit-learn.org), and Python Image Library – PIL – (http://www.pythonware.com/products/pil/) librariesinstalled.Anoteaboutthesoftwareisprovidedas

Supplementarymaterial(SoftwareUsesupplementary.pdf).

Fig.1–Resultsobtainedbyconsideringonlytheaddresses onthemapasdatasets.Noweightisassignedtoeach addressonthebasisofthenumberofrecordedcases.

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Results

and

discussion

Fig. 1 shows the results obtained by considering only the addressesonthemapasdatasets,correspondingtothe anal-ysisbyLeComberetal.,9_{thatis,noweightwasassignedtoan}

addressonthebasisofthenumberofrecordedcases.InFig.2

weshowtheGPanalysiswithweightsassignedtoeachpoint ofthemaponthebasisofthenumberofcases.Theresult isquitestriking,sincetheredarea,representingtheareaof themapwiththepointswith95%ofhighestprobability com-prisedthepumpofBroadStreet.Thisareawasabout30min diameter.Withrespecttothemethodthatdoesnotconsider thenumberofcasesasweights(showninFig.1),thetotalarea ofhighestprobabilityofthepresenceofthesourcewashence muchsmaller.

Countingthepixelswithhighestprobabilityoffindingthe sourceof the crimes, we found that the red pixels (those withhighestprobability)decreasedsubstantiallypassingfrom consideringonlytheaddressestousingthewholedataset withweights,that isfrom 36533to10068 (visiblefrom the reductionindimensionoftheredareafromFig.1toFig.2).

Fig.2–GPanalysiswithweightsassignedtoeachpointof themaponthebasisofthenumberofcholeracases.The redarea(thatwithhighestprobabilitytofindtheinfection source)isonlyabout30mindiameteranditcomprisesthe famouspumpofBroadStreet.

Calculatingeachcaseasasinglepoint,alsoiflocatedinthe samepositiononthemap(thatisatthesameaddress), pro-ducedanareaofredpixelsonlyslightlyhigherwithrespect totheuseofweights(datanotshown).

Calculatingthedistanceonthemap,theGPanalysiswith weightsproducedanareaofmaximumprobabilityoffinding thesourceofabout30mindiameter,whichcontainsthewell knownsourceofcholeracasesinLondon,thatisthefamous pumpofBroadStreetrecognizedbySnow.12_{Thisresultshows}

thattheuseofweightsproportionaltothenumberofcases ineachaddress largelyincreasetheprecisionofthe analy-sis,thatis,itreducestheareaofmaximumprobabilitywhere tolookforthesourcewithrespecttootherGPtechniquesas thoseemployedbyLeComberetal.9_{andVerityetal.}11

Conclusion

Theweightedgeoprofilingcanbeausefulmethodtoidentify acenteroforiginofanoutbreakofadisease,incaseswhen morecasesofinfectioncanbefoundinthesamepointofthe map(normallycorrespondingtoaresidence),largelyreducing theprioritypointsandhenceshowingthehighestprecisionin delimitingthesourcesearcharea.

Theuseofweightsformorecasesofinfectionsatthesame address,canbeagoodchoiceonlyincaseswheresecondary person-to-personinfectionscanbeconsiderednotprobable (asitislikelythecaseofcholera),otherwise,asstatedbyLe Comberetal.9_{itisnecessarytouseasinputdataeachaddress}

(pointonthemap)aspointswiththesameweight=1.

Funding

FinancialsupportbytheItalianMinistryofResearch(MUR), FondidiAteneo.

Conflicts

of

interest

Theauthorsdeclarenoconflictsofinterest.

Appendix

A.

Supplementary

data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.bjid.2016.09.010.

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