I.J.ModernEducationandComputerScience,2017,11,49-57PublishedOnlineNovember2017inMECS()DOI:10.5815/ijmecs.2017.11.06Copyright©2017MECSI.J.ModernEducationandComputerScience,2017,11,49-57ModelingtheeffectofNetworkAccessControlandSensorRandomDistributiononWormPropagationChukwuNonsoH.NwokoyeDepartmentofComputerScience,NnamdiAzikiweUniversity,Awka,NigeriaEmail:explode2kg@yahoo.comNjidekaMbeledogu,IkechukwuI.Umeh,Ihekeremma,A.EjimoforDepartmentofComputerScience,NnamdiAzikiweUniversity,Awka,NigeriaEmail:njidembeledogu@yahoo.com,ikumeh1@gmail.com,iaejims2@yahoo.comReceived:31July2017;Accepted:24October2017;Published:08November2017Abstract—Sensornetworksareappealingtargetsformaliciousattacksthatinvadethenetworkwiththeaimofdepletingtheconfidentiality,availabilityandintegrity(CIA)features/parametersofneighboringsensornodes.Thisisduetoitsopencommunication,minimalresourcesanditsdeploymentinun-trusted,unguardedandunfriendlyterrains.Torestrictillegitimateusersormaliciousattackers(suchasworms)networkanalystshavesuggestednetworkaccesscontrol(NAC).Specifically,weapplyNACtowirelesssensornetworkepidemicmodelsinordertoinvestigatedistributiondensity,transmissionrangeandsensorarea/field.Ouranalysesinvolvedanalyticalexpressionsoftwosensorfieldsgleanedfromliterature.Additionally,weexploredthepossibilitiesofinfectivityofsensornodesattheexposedclassusingthetwoexpressionsforsensorfieldtopologies.Wealsoderivedthereproductionratiosandsolutionsatseveralequilibriumpointsforthemodels.Itisourhopethatthatourworkhereinwouldimpactsensordeploymentdecisionsfororganizationsthatutilizewirelesssensornetworksformeaningfuldailyactivities.IndexTerms—EpidemicTheory,WirelessSensorNetworks,NetworkAccessControl,RandomDistribution.I.INTRODUCTIONTheimmenseusesofWirelessSensorNetworkshavemadeitaprominenttechnologyofthisera.Thiskindofnetworksmostlyallowstherandomdeploymentofsensornodesinun-trustedterrainswithoutpredeterminedorengineeredposition.Thisemergingtechnologyconsistsofminiaturizedbutlowbattery-powereddevicesthatincorporateminimalsensing,processing,computationandradiotransmissioncapabilities[1].Itshugepotentialisevidentlyseeninitsabilitytoprovidedynamicandadaptablearchitecturesfordiverseapplicationsinhomes,healthcare,industryandinthemilitary[1],[2].Specifically,WSNapplicationsareseeninthemilitary(formonitoringforces/equipments,battlefieldsurveillance,reconnaissance,targeting,battledamageevaluation);thehomeandintheenvironment(forbiocomplexitymapping,precisionagriculture,fireandflooddetectionetc)[1,3].Itsuseextendsalsotohealthapplications(fortelemonitoringofdata,tracking/monitoringofdoctors/patientsanddrugadministration)andothercommercialapplications[3].AsshowninFig1,WSNsare“multi-hoppacketbasednetworks”[4]thatconsistsofsensornodeswhicharedistributedinasensorfieldwheretheyarewirelesslyconnectedtothesink[5].Theytrack,recordandsendambientterritorialparameterstoadatacollector(orbasestation)through“multihopinfrastructureless”transmissionbetweenneighboringsensornodes.Thecommunicationdoneintheopenairmedium[4]anditsdeploymentinun-trusted,unguardedandunfriendlyterrain,makestheWSNaneasytargettoexternalattacksthatseektodelay/disruptlegitimateflowofinformation.TheseattackersexploitotheropenchallengesoftheWSNsuchasfinitebandwidth,computationalpower,storage,andcommunicationrange;packets’authentication,anduncertainty(inmobility,topologycontrol,density,sensingaccuracy)[1,3].Modernresearch-baseddevelopmentsinsensornetworksindicatethatamalevolentattackercanutilizeseveralinnardsofsensornodestooutspreadmaliciouscodesallthroughthenetworkwithoutphysicalcontactorhumanintervention[6].AsGiannetsosetal.[6]putsit,“suchamethodistoexploitmemoryrelatedvulnerabilities,likebufferoverflows,tolaunchawormattack”.Attackssuchassinkhole,sybil,wormholeandhellofloodinWSNareeventsthatdiminishesoreliminatesanetwork'scapacitytoperformitsexpectedfunction[7];inotherwordstheseattacksdepletetheconfidentiality,availabilityandintegrity(CIA)parametersofneighboringsensornodes.Tocurbincidencesofmaliciouscodeattacksinnetworks,analystshaveproposedequation-basedmodelstocharacterize,representandunderstandspreadpatterns,strategies.50ModelingtheeffectofNetworkAccessControlandSensorRandomDistributiononWormPropagationCopyright©2017MECSI.J.ModernEducationandComputerScience,2017,11,49-57Oftentimesthestrengthofparticularmodelisdeterminedbyhowmuchitcanenhanceunderstandingofmaliciouscodetransmission.Fig.1.WirelessSensorNetworksEnvironment[32]II.RELATEDWORKSResearchersinnetworksecurityhavediscoveredthatthereexistsimilarfeaturesbetweenvirusspreadinbiologicalnetworksandthepropagationofmaliciouscodesintelecommunicationnetworks.WiththedevelopmentofthewidelyappliedSusceptible-Infected-Removed(SIR)analyticalmodel[8-10],thejourneyintoinvestigatingtheinfectiousoutcomesofasusceptiblepopulationinviewoftheinteractionbetween“agent”,“host”and“environment”began.Usuallyreferredtoas“Epidemicmodels”,thesesystem(s)ofequationsthatimplementtheepidemictheorycanbeordinarydifferential,partialdifferential,ordifferenc