Consider the propagation of a contagion process (“epidemic") on a network, modeled as a controlled SIS process. We study the problem of allocating a fixed curing budget to the nodes of the graph in real time. The allocation policy  is dynamic; it exploits the knowledge of the state of each node as well as the network structure. This is a representative problem of closed-loop control of the stochastic evolution of a process over a network. We discuss various problems of this type, some results, and some general research directions.