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The recent observations of muon charge ratio up to about 10 TeV and ofatmospheric neutrinos up to energies of about 400 TeV has triggered a renewedinterest into the high-energy interaction models and cosmic ray primarycomposition. A reviewed calculation of lepton spectra produced in cosmic-rayinduced extensive air showers is carried out with a primary cosmic-ray spectrumthat fits the latest direct measurements below the knee. In order to achievethis, we used a full Monte Carlo method to derive the inclusive differentialspectra (yields) of muons, muon neutrinos and electron neutrinos at the surfacefor energies between 80 GeV and hundreds of PeV. The air shower simulator {\sccorsika} 6.990 was used for showering and propagation of the secondaryparticles through the atmosphere, employing the established high-energyhadronic interaction models {\sc sibyll} 2.1, {\sc qgsjet-01} and {\scqgsjet-ii 03}. We show that the performance of the interaction models allowsmakes it possible to predict the spectra within experimental uncertainties,while {\sc sibyll} generally yields a higher flux at the surface than theqgsjet models. The calculation of the flavor and charge ratios has lead toinconsistent results, mainly influenced by the different representations of theK/$\pi$ ratio within the models. Furthermore, we could quantify systematicuncertainties of atmospheric muon- and neutrino fluxes, associated to themodels of the primary cosmic-ray spectrum and the interaction models. For mostrecent parametrizations of the cosmic-ray primary spectrum, atmospheric muonscan be determined with an uncertainty smaller than $^{+15}_{-13}$% of theaverage flux. Uncertainties of the muon- and electron neutrino fluxes can becalculated within an average error of $^{+32}_{-22}$% and $^{+25}_{-19}$%,respectively.

Influence of hadronic interaction models and the cosmic ray spectrum on the high energy atmospheric muon and neutrino flux