  Extinction of small metallic spheres has been well understood through the
classical Mie theory when the host medium is dispersive and transparent.
However, the role of host dissipation on the particulate extinction remains a
competition between the enhancing and reducing effects on the localized surface
plasmonic resonance (LSPR). Here, using a generalized Mie theory, we elaborate
on the specific influence mechanisms of host dissipation on the extinction
efficiency factors of a plasmonic nanosphere. To this end, we isolate the
dissipative effects by comparing the dispersive and dissipative host with its
transparent counterpart. As a result, we identify the damping effects of host
dissipation on the LSPR including the resonance widening and amplitude
reducing. The resonance positions are shifted by host dissipation, which cannot
be predicted by the classical Fr\"ohlich condition. Finally, we demonstrate
that a wide-band extinction enhancement due to host dissipation can be realized
away from the positions of LSPR.
