  Secondary astrophysical production of $e^+$ and $\bar{p}$ cosmic rays is
considered. Inclusive $\pi$, $K$, and $\bar{p}$ production cross sections in
$pp$ collisions at large $\sqrt{s}$ are parametrised using recent experimental
data at LHC energies. The astrophysical production rate ratio
$Q_{e^+}/Q_{\bar{p}}$ is calculated for an input cosmic ray proton flux
consistent with local measurements. At $10<E<100$$\sim$GeV the cosmic ray flux
ratio $J_{e^+}/J_{\bar{p}}$ measured by AMS02 falls below the production rate
ratio by about 50\%, while at high energy $E>100$$\sim$GeV the measured flux
ratio coincides with the production rate ratio of the secondary source.
