  Faults and viruses often spread in networked environments by propagating from
site to neighboring site. We model this process of {\em network contamination}
by graphs. Consider a graph $G=(V,E)$, whose vertex set is contaminated and our
goal is to decontaminate the set $V(G)$ using mobile decontamination agents
that traverse along the edge set of $G$. Temporal immunity $\tau(G) \ge 0$ is
defined as the time that a decontaminated vertex of $G$ can remain continuously
exposed to some contaminated neighbor without getting infected itself. The
\emph{immunity number} of $G$, $\iota_k(G)$, is the least $\tau$ that is
required to decontaminate $G$ using $k$ agents. We study immunity number for
some classes of graphs corresponding to network topologies and present upper
bounds on $\iota_1(G)$, in some cases with matching lower bounds. Variations of
this problem have been extensively studied in literature, but proposed
algorithms have been restricted to {\em monotone} strategies, where a vertex,
once decontaminated, may not be recontaminated. We exploit nonmonotonicity to
give bounds which are strictly better than those derived using monotone
strategies.
