Prophylaxis of Epidemic Spreading with Transient Dynamics

We investigate the containment of epidemic spreading in networks from a normative point of view. We consider a susceptible/infected model in which agents can invest in order to reduce the contagiousness of network links. In this setting, we study the relationships between social efficiency, individual behaviours and network structure. First, we exhibit an upper bound on the Price of Anarchy and prove that the level of inefficiency can scale up to linearly with the number of agents. Second, we prove that policies of uniform reduction of interactions satisfy some optimality conditions in a vast range of networks. In setting where no central authority can enforce such stringent policies, we consider as a type of second-best policy the shift from a local to a global game by allowing agents to subsidise investments in contagiousness reduction in the global rather than in the local network. We then characterise the scope for Pareto improvement opened by such policies through a notion of Price of Autarky, measuring the ratio between social welfare at a global and a local equilibrium. Overall, our results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design efficient containment policies.