Individual Non-Pharmaceutical Intervention Strategies for Stochastic Networked Epidemics

Unlike the vast majority of works that study the spread of epidemic processes in search of top-down policy recommendations or resource allocation strategies in eradicating an unwanted virus, in this paper we instead consider how the virus spreads at the person-to-person level. More specifically, based on the locally available information to a particular person, how should that person make use of this information to better protect themself? 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. 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.