  This paper revisits a longstanding problem of interest concerning the
distributed control of an epidemic process on human contact networks. Due to
the stochastic nature and combinatorial complexity of the problem, finding
optimal policies are intractable even for small networks. Even if a solution
could be found efficiently enough, a potentially larger problem is such
policies are notoriously brittle when confronted with small disturbances or
uncooperative agents in the network. Unlike the vast majority of related works
in this area, we circumvent the goal of directly solving the intractable and
instead seek simple control strategies to address this problem. More
specifically, based on the locally available information to a particular
person, how should that person make use of this information to socialize as
much as possible while ensuring some desired level of safety? We set this up as
a finite time optimal control problem using a well known exact Markov chain
Susceptible-Infected-Removed (SIR) model. Leveraging results from the
literature, we employ a commonly used mean-field approximation (MFA) technique
to relax the problem. We show solution of this problem to be a form of
threshold on the chance of infection of the neighbors of that person.
Simulations illustrate our results.
