简介：Inthispaperthefixedpointindexproblemforaclassofpositiveoperatorswithboundarycontrolconditionsisdiscussed,andsomesufficientconditionsforthefixedpointindextobeequalto1or0aregiven.Moreover,ageneralfixedpointtheoremofexpansionsandcompressionsforconeisobtained,whichgeneralizesandimprovesthecorrespondingresultsof[3,8,9].Asanapplication,weutilizetheresultspresentedabovetostudytheexistenceconditionsofpositivesolutionsofnonlinearintegralequationsmodellinginfectiousdiseases.
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