  A function is strongly non-recursive (SNR) if it is eventually different from
each recursive function. We obtain hierarchy results for the mass problems
associated with computing such functions with varying growth bounds. In
particular, there is no least and no greatest Muchnik degree among those of the
form SNR$_f$ consisting of SNR functions bounded by varying recursive bounds
$f$.
  We show that the connection between SNR functions and canonically immune sets
is, in a sense, as strong as that between DNR (diagonally non-recursive)
functions and effectively immune sets. Finally, we introduce pandemic
numberings, a set-theoretic dual to immunity.
