Self-improving immunization policies for complex networks

To design efficient immunization strategies against viruses, we have to be aware of the properties of the graphs in which viruses spread. We review the properties found in many real-world graphs, such as small-world and scale-free, and the deterministic models that exhibit them. As a virus is an independent entity, our modeling takes into consideration parameters related to agents, such as their heuristics and their memory. We perform a 2k factorial design to identify the contribution of the parameters of the agents and the properties of the topology. To benefit from the potential of agents to immunize dynamic networks, we specify a multi-agent system: the agents observe their environment, exchange their knowledge with minimal communication cost and fast consensus, and thus have a model of the dynamics that allows them to cope with changes. We present an algebraic framework that allows such exchange of knowledge while providing rigorous characterization.