An Agent Based Distributed Control for Networked SIR Epidemics
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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.