  Increasing connectivity of communication networks enables large-scale
distributed processing over networks and improves the efficiency for
information exchange. However, malware and virus can take advantage of the high
connectivity to spread over the network and take control of devices and servers
for illicit purposes. In this paper, we use an SIS epidemic model to capture
the virus spreading process and develop a virus-resistant weight adaptation
scheme to mitigate the spreading over the network. We propose a differential
game framework to provide a theoretic underpinning for decentralized mitigation
in which nodes of the network cannot fully coordinate, and each node determines
its own control policy based on local interactions with neighboring nodes. We
characterize and examine the structure of the Nash equilibrium, and discuss the
inefficiency of the Nash equilibrium in terms of minimizing the total cost of
the whole network. A mechanism design through a penalty scheme is proposed to
reduce the inefficiency of the Nash equilibrium and allow the decentralized
policy to achieve social welfare for the whole network. We corroborate our
results using numerical experiments and show that virus-resistance can be
achieved by a distributed weight adaptation scheme.
