Optimal control of information epidemics

In this work we address two problems concerning information propagation in a population: a) how to maximize the spread of a given message in the population within the stipulated time and b) how to create a given level of buzz- measured by the fraction of the population engaged in conversation on a topic of interest- at a specified time horizon. Arising in the context of two rather disparate networks- social and wireless vehicular networks, their importance in campaigning on social networks and security in vehicular networks can only be understated. Taking a mean-field route, we pose the two problems as continuous-time deterministic optimal control problems. We characterize optimal controls, present some numerical results and provide practical insights. Interestingly, the problems we address are antithesis to those in disease epidemics, which need to be contained rather than actively spread.