Eradicating Ebola.docx

Eradicating Ebola.docx

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EradicatingEbola

EradicatingEbola

Abstract

TotackletheissuesoncureofEbola,weselectWestAfricaasasampleandinitiateourinvestigationfromthreebasicpoints,thatis,transmissionofEbolavirusdisease,transportquantityofvaccineandtransportationmeans.Foreachofthem,wedeviseanelementarymodelforanalysis.

Undertheassumptionthattransmissionareasarefixed,weestablishourfirstmodeltodescribethetransmissionofEbolavirus.Thenwebuildthesecondmodeltocalculatetherequirementofvaccineandthetransportquantitydemandedvirtuallyaccordingtothetransmissionconditionsobtainedfromthefirstmodel.Nextconsideringthetransportquantityandthelocationofdestinations,wespecifythethirdmodeltodiscussthetransportationmeans.Inthiswaywegaintheoptimalconfigurationfortheissues.

Furthermore,toexaminethereasonablenessofourresults,wecomparethesedatatotheresultsontheInternet.Anditundoubtedlyshowsthatourmodelscanbeappliedinpracticalutility.

Thuswedrawaconclusiononoptimalconfigurationfortheissues.

Finallywehaveprepareda1-2pageletterthatexplainsourresultsandinvolvesanon-technicalexplanationofourmathematicalmodelsthatstaffsinWHOcancomprehend.

Keywords:

transmissionofEbolavirus,transportquantityofvaccine,transportationmeans,elementarymodel

Contents

Abstract1

Contents2

Ⅰ.Introduction3

1.1Background2

1.2GenusEbolavirus2

1.3Sourceofhumaninfection2

1.4Evidenceofhuman-to-humantransmission2

1.5Signsandsymptoms2

1.6Diagnosisandtreatments2

1.7EbolavirusbreakingoutinWestAfrica2

Ⅱ.Analysisfortheissues3

Ⅲ.Thebasicassumptions3

Ⅳ.Nomenclature3

Ⅴ.Ourmodel13

5.1Modelanalysis2

5.2Modelestablishing2

5.3Modelsolution2

5.4Testofmodel’sapplication2

Ⅴ.Ourmodel13

Ⅰ.Introduction

Ebolavirus,aparticularlyfatalviruswhichleadstoEbolahaemorrhagicfever,firstappearedin1976intwosimultaneousoutbreaksinNzara,Sudan,andinYambuku,DemocraticRepublicofCongo（formerlyZaire）andhasraisedgreatconcerninmedicalfieldfromthenon.Ebolavirusiscontagiousbothtomankindandnon-humanprimates.Itresultsinfever,shockandmultipleorganfailureandexhaustspeopletodie.Sofar,accordingtothedatagivenbyWorldHealthOrganization（WHO）,thefatalityrateforEbolavirushasbeenrecordedtobehighastoninetypercent.

1.1Background

ThenameEbolacomesfromariverinthenorthofDemocraticRepublicofCongo.In1976,ascarcevirusappearedthere,attackingfifty-fivevillagesnearbyandcausingthousandsofdeaththatalmostnoonesurvived.EverafterthattheEbolaistakentodescribethisseverevirus.Andthreeyearslater,EbolacamebackandsweptSudan.Afterthesetwocruelplagues,Ebolavanishedforfifteenyears.

1.2GenusEbolavirus

GenusEbolavirusisoneofthreemembersoftheFiloviridaefamily（filovirus）,alongwithgenusMarburgvirusandgenusCuevavirus.Andsofarhumanhasspecifiedfivedistinctspecies:

•ZaireEbolavirus（EBOV）

•BundibugyoEbolavirus（BDBV）

•SudanEbolavirus（SUDV）

•TaiForestEbolavirus（TAFV）

•RestonEbolavirus（RESTV）

BDBV,EBOV,andSUDVhavebeenassociatedwithlargeEbolavirusdiseaseoutbreaksinAfrica,whereasRESTVandTAFVhavenot.

Thosespeciesdifferinpathology.EBOVandSUDVarefoundedfatalbothtomankindandnon-humanprimates,whileBDBVhasnoobviousinfluenceonmankindbutisstillfataltonon-humanprimates.TheRESTVspecies,foundinPhilippinesandthePeople’sRepublicofChina,caninfecthumans,butnoillnessordeathinhumansfromthisspecieshasbeenreportedtodate.

1.3Sourceofhumaninfection

•FruitbatsaresuspectedasthenaturalhostforEbolavirus.AccordingtothereportsfromCableNewsNetwork（CNN）andDailyMail,theEbolavirusdiseaserecentlyspreadinginWestAfricamayoutbreakfrom2-year-oldchildbittenbyafruitbat.Theysaid,thechildwasbittenbyafruitbatandthendiedfourdayslater,on6December2013.Afterhisdeath,hismotherinitiatedbleedingsymptomanddiedon13December2013.Thenitcametothosewhohadattendedtheirfuneral.Afterthatarethevillagesnearby.Inthatway,theplagueextendstothewholeWestAfrica.

•Non-humanprimateshavebeenconsideredasasourceofEbolavirus.However,adecadeagotheyweresubstantiatedtobeanaccidentalhostjustlikehumanbeings.

1.4Evidenceofhuman-to-humantransmission

Ebolavirusinfestswildanimals.Viaclosecontactwithinfectedanimalssuchastheblood,secretionsandotherbodilyfluids,Ebolavirusisbroughtintohumancommunity.Andthen,throughdirectcontacts（brokenskin,mucousmembraneswiththeblood,secretionsetc.）andindirectcontacts（environmentscontaminatedwithfluids）,Ebolaviruscontinuesitstransmissionamonghumans.

Andthevirusequipsnoinfectiousnessduringtheincubationperiod（varyingfrom2to20days）andbecomescontagiousonceahostpresentswithsymptoms.

Thevirusremainsinthesemenofpersonswhohaverecoveredfromthediseaseforthreemonthsafterrehabilitation.

1.5Signsandsymptoms

•Duringtheincubationperiod,infectedpersonsdon’tfeelsickuntilonsetofsymptoms.

•Ebolavirususuallycomeswithsuddenonsetoffever,intenseweakness,musclepain,headache,nauseaandsorethroat.Thenthefollowingsymptomslikevomiting,diarrheaarise.Finallypatientswilldieinorganfunctionsimpaired.

1.6Diagnosisandtreatments

•DefinitivediagnosisofEVDismadethroughlaboratorytestingbecauseofinfectionrisk.Laboratoryfindingsfrequentlyincludelowwhitebloodcellandplateletcountsandelevatedliverenzymes.

•Uptonow,therearenolicensedEbolavaccinesbut2potentialcandidatesareundergoingevaluation.

•Earlysupportivecarewithrehydration,symptomatictreatmentimprovessurvival.Thereisasyetnolicensedtreatmenttestifiedtoannihilatethevirusbutarangeofblood,immunologicalanddrugtherapiesareunderdevelopment.

1.7EbolavirusbreakingoutinWestAfrica

EbolavirusbreaksoutinWestAfricainFeb2015.Tillnow,basedonthereportsonEbolafromWHO,ithasalmostsweptthewholeWestAfrica,especiallyincountrieslikeGuinea,SierraLeoneandLiberia.EvendistantcountriessuchasUSA,SpainandUKhavebeeninvolvedinthisdisaster.Asisreportedtodate,Ebolahasposed22495casesofEbolavirusdiseaseand8981deathscumulatively.

Figure1.MapofEbolacasesovertheworld

Figure2.DistributionofEbolacaseovertheworld

Ⅱ.Analysisfortheissues

2.1Spotsselectedforexperiment

Ebolavirustransmitsendemically,andusuallyitisrestrictedinthetropicalrainforestsofcentralAfricaandthesteppesofsoutheastAfricabyspecificenvironmentalconditions.ThoseyearsthiskindofvirushasspreadfromtheinitiateSudanandCongotoothercountriesnearbysuchasCentralAfrican,LibyaandGabon.

Nevertheless,incountriesdistantfromAfricasuchasUSAandSpain,casesofEbolavirusdiseaseoccuraccidentallybutareallattributedtoimportinfection.Tosomeextent,itshowsthevirustransmitsinspecificregions.Inotherwords,thevirustransmitsendemicallyandwillnotfindanyotherareasuitableforitsbreedbecauseitisrestrictedbyspace.

ThereforeweselectthreecountriesGuinea,SierraLeoneandLiberia,wheretheEbolaviruscasesoccurmostfrequently,asasample.

Andhereisasurveyonpopulationsofdistinctregionsinthesethreecountries.

Figure3.PopulationdistributionsofdistinctregionsinGuinea,SierraLeoneandLiberia

Guinea

Population

SierraLeone

Population

Liberia

Population

G1

289,000

S1

274,118

L1

276,863

G2

165,000

S2

452,095

L2

127,076

G3

284,000

S3

549,924

L3

83,388

G4

82,000

S4

256,686

L4

84,119

G5

131,000

S5

1,345,142

L5

1,118,241

G6

156,000

S6

418,184

L6

333,481

G7

286,000

S7

352,048

L7

462,026

G8

136,000

S8

570,283

L8

209,923

G9

421,000

S9

404,036

L9

221,693

G10

246,000

S10

151,979

L10

71,509

G11

156,000

S11

156,388

L11

102,391

G12

114,000

S12

537,864

L12

125,258

G13

160,000

S13

387,824

L13

66,789

G14

244,000

L14

57,913

G15

167,000

L15

135,938

G16

744,000

G17

235,000

G18

188,000

G19

296,000

G20

278,000

G21

87,000

G22

124,000

List1.Populationsofcorrespondingregions

Ⅲ.Thebasicassumptions

Ⅳ.Nomenclature

Ⅴ.Ourmodel1

5.1Modelanalysis

WiththedeteriorationofEboladisease,peopleininfectedareademandmoremedicine.Thusweassumemedicinequantitydemandedkeepstwotimesofthequantityofinfectedcases（exceptthedeaths）.

Asforthepopulationvariableofinfectedpeople,wecanconfirmthedynamicrelationbetweenpopulationandtimebyutilizingRISmodel（transmissionmodelofinfectiousdisease）.

5.2Modelestablishing

PeoplecontractEbolavirusdiseaseviadirectandindirectcontacts.Inourinvestigation,forsimplicity,weassume:

1.Identicalrisksthatdistinctpeoplegetinfected.

2.Thosewhogetinfectedwillnotbeseparatedordieinstantly.

3.Weeliminateotherfactorssuchasbirth,naturaldeathandimmigrationintheseregions.

4.Thecorrespondinginfectivityofcontactfrequencyisfixed.

5.Regardlessofsolitude,peopleintermingleuniformly.

Thuswedividethepeopleintothreegroups:

1.ClassS:

healthypeople,itisagroupofpeoplewhoaren’tinfectedbuthaverisksofbeinginfected.

2.ClassI:

infectedpeople,itisagroupofpeoplewhocontractEbolavirusandcaneasilytransmitthedisease.PeopleinthisclasscanbecuredandtransferredintoClassR.

3.ClassR:

peoplewhohavegone,