Abstract:
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
better protect their self? How can that person socialize as much as possible while ensuring
some desired level of safety? More formally, the solution to this problem requires a rigorous
understanding of the trade-off between socializing with potentially infected individuals and
the increased risk of infection. We set this up as a finite time optimal control problem using a
well known exact Markov chain compartmental Susceptible-Infected-Removed (SIR) model.
Unfortunately, the problem set up is intractable and requires a relaxation.
Leveraging results from the literature, we employ a commonly used mean-field approximation
(MFA) technique to relax the problem. However, the main contribution distinguishing
our work from the myriad works which study networked MFA models is that we verify
the effectiveness of our solutions on the original stochastic problem, rather than the relaxed
problem. We find that the optimal solution of the problem to be a form of threshold on the
chance of infection of the neighbors of that person. Simulations illustrate our results.
