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1、NonlinearAnalysis:ModellingandControl,2010,Vol.15,No.1,97–108Analysisofadelaynonautonomouspredator-preysystemwithdiseaseinthepreyG.P.SamantaMathematicalInstitute,SlovakAcademyofSciencesStefanikova49,81473Bratislava,SlovakRepublicgpsamanta@yahoo.co.ukReceived:2009-08
2、-01Revised:2010-01-14Publishedonline:2010-03-04Abstract.Inthispaperwehaveconsideredanonautonomouspredator-preymodelwithtimedelayduetogestation,inwhichadiseasethatcanbetransmittedbycontactspreadsamongthepreyonly.Here,wehaveestablishedsomesufficientconditionsontheperma
3、nenceofthesystembyusinginequalityanalyticaltechnique.ByLyapunovfunctionalmethod,wehavealsoobtainedsomesufficientconditionsforglobalasymptoticstabilityofthismodel.Wehaveobservedthatthetimedelayhasnoeffectonthepermanenceofthesystembutithasaneffectontheglobalasymptotics
4、tabilityofthismodel.Theaimoftheanalysisofthismodelistoidentifytheparametersofinterestforfurtherstudy,withaviewtoinformingandassistingpolicy-makersintargetingpreventionandtreatmentresourcesformaximumeffectiveness.Keywords:ecoepidemiology,susceptibleandinfectedprey,pr
5、edator,permanence,Lyapunovfunctional,globalstability.1IntroductionThemathematicalepidemicmodelshavereceivedmuchattentionfromresearchersaf-terthepioneeringworkofKermack-McKendrick[1]onSIRS(susceptible-infective-removal-susceptible)systems,inwhichtheevolutionofadiseas
6、ewhichgetstransmitteduponcontactisdescribed.Ecologyandepidemiologyaretwomajoranddistinctfieldsofresearchintheirownright.Lotka[2]andVolterra[3]establishedseminalworksonthemathematicalmodellingofpredator-preyandcompetingspeciesintermsofsimultaneousnon-lineardifferentia
7、lequations,makingthefirstbreakthroughinmodernmathematicalecology.Ecoepidemiologyisthestudyofinteractingspeciesinwhichadiseasespreads.ThestudyofEcoepidemiologyhasimportantecologicalsignificance.Ecoepidemiologyresearchisbecomingimportantasitinvolvespersistence-extinctio
8、nthresholdofeachpopulationinsystemsoftwoormoreinteractingspeciessubjectedtoparasitism[4–8].Inthenaturalworld,however,speciesdonotexistalon
