  The spread of fake news on online social networks (OSNs) has become a matter
of concern. These platforms are also used for propagating important authentic
information. Thus, there is a need for mitigating fake news without
significantly influencing the spread of real news. We leverage users' inherent
capabilities of identifying fake news and propose a warning-based control
mechanism to curb this spread. Warnings are based on previous users' responses
that indicate the authenticity of the news. We use population-size dependent
continuous-time multi-type branching processes to describe the spreading under
the warning mechanism. We also have new results towards these branching
processes. The (time) asymptotic proportions of the individual populations are
derived using stochastic approximation tools. Using these, relevant type 1,
type 2 performances are derived and an appropriate optimization problem is
solved. The proposed mechanism effectively controls fake news, with negligible
influence on the propagation of authentic news. We validate performance
measures using Monte Carlo simulations on network connections provided by
Twitter data.
