Consider the following game between a worm and an alert
over a network of $n$ nodes. Initially, no nodes are infected or alerted
and each node in the network is a special detector node independently
with small but constant probability, $\gamma$. The game starts with a single node
becoming infected. In every round thereafter, every infected node sends
out $\beta$ worms to other nodes in the population for some constant $\beta$;
in addition, every alerted node sends out $\alpha$ alerts for some constant $\alpha$.
Nodes in the network change state according to the following three rules: 1) If a worm
is received by a node that is not a detector and is not alerted, that node
becomes infected; 2) If a worm is received by a node that is a detector,
that node becomes alerted; 3) If an alert is received by a node that is not
infected, that node becomes alerted.
We allow an infected node to send worm messages to any other node in the network, but, in contrast,
allow the alerts to only be sent over a special precomputed overlay network where every node has $O(\log{n})$ degree.
We assume that the infected nodes collaborate with each other, and know everything except which
nodes are detectors, and the alerted nodes' random coin flips.
We show, for this game, that it is possible to design an algorithm that can prevent any worm from infecting more
than a vanishingly small fraction of the nodes in logarithmic time.
In particular, we describe an algorithm and a network that ensures with high probability that atmost o(n) nodes can be infected in $O(\log{n})$ time steps by any worm for $\alpha$ a fixed constant depending only on $\beta$ and $\gamma$.
In addition, our algorithm ensures that the
number of nodes that may receive a spuriously generated ``false alert'' is polylogarithmic in $n$.
We complement our theoretical analysis with simulations on networks of size up to $2^{25}$.