Math583-ClassProject-Spring1995 AntibioticResistance Thisprojectconcernssomepracticalissuesinthespreadofantibioticresistanceforcertainhuman pathogens,andalternativeschemestoalleviatethespread(seeScience265:589andScience266:1462).It thuswillincludeaspectsofepidemiologyofdisease,populationgenetics,andspatialspread.Inparticular, wewoulddealwithwhatoccursunderselectiontoresistantstrainsifanti-bioticuseisrestricted,and whattheeffectswouldbeofgeneflowwhennewindividualscarryingresistantstrainsmoveintoacommunitywhichrestrictsantibioticusetocontrolresistantstrains.Thekeyquestionshereare(a)canwecharacterizeonwhattimescalerestrictionofantibioticusewithinacommunitywillbeeffectiveinreducing healthrisksfromresistantstrains;(b)whatwouldbetheeffectof"rotationstrategies"inwhichseveral antibioticswererotatedinuseinalocalregiontocontrolbacterialpathogens;(c)howdothepatternsof spatialmovementofindividualsbetweenregionsaffecttheseresults-e.g.howmuchgeneflowwillswamp outthebenefitsofrestrictingantibioticuse;and(d)isitpossibletodevise"spatially-varyingrotation strategies"forantibioticusethatamelioratetheeffectsofgeneflow.Thisprojectwillinvolvedigginginto literatureonantibioticresistance,developingalocalmodelforresistancespreadandcontrolbyantibiotics (theremaybeasomemodelsalreadyconstructedforthis),developingmethodstocouplelocalmodels togetherduetogeneflow,andpossiblyaddingtothissomecontrolmodelthatallowsvariationincontrol variablessuchastheperiodsforantibioticuseand/orrotation. Tasks: 1.Literaturereviewonantibioticresistanceepidemiology.Thisrequiresgoingtobasicjournalstoget background,contactingappropriateresearchers(e.g.attheCDCinAtlanta),providingasummaryforthe entireclass,andservingassourceofreferencesforbiologicalquestionsassociatedwiththeproject.(1person) 2.Literaturereviewofepidemiologicalmodelingthatmaybeappropriateforustouseasastartingpoint. Thisrequiresgoingtojournalstogetbackground,consideringalternativemodelingapproacheswhichhave beenusedforspatialaspectsofepidemics,lookingatthepesticideresistancemodelingliterature(seefor exampletheexampleinPopulus),servingasreferencepersonformodelingaspectsoftheproject,andprovidingasummarytotheentireclass.(2people) 3.Deriveamathematicalformulationoftheproblem,carefullylistingallassumptionsintheformulation, andexplicitlyconsideringavarietyofalternativeassumptionsforvariouscomponentsofthemodel.(2 people) 4.Carryoutacompletemathematicalanalysisofthemodeldescribedin#3,usinganalyticalmethods whenpossibleandcomputationalmethodswhenappropriate,includinganynecessarycoding.Summarize theresultsoftheanalysisandhowalternativeassumptionsmightmodifythem.(2people) 5.Writeacompletereportoftheentireproject,inaformsuitableforpublicationinanappropriatejournal.(1person) KeyReference:Ewald,PaulW.EvolutionofinfectiousdiseaseOxfordUniversityPress,1994.UTKCall #RC112.E931994(onovernightreserve)