The Costs of Overcrowding (and Release): Strategic Discharges for Isolated Facilities During Epidemiological Outbreaks

Abstract

For isolated, densely populated facilities, such as prisons and nursing homes, it is difficult to enact social distancing measures when catastrophic epidemiological outbreaks occur. In such facilities, strategic releases can enhance social distancing, yet have inherent costs, e.g., the potential for recidivism in crime for prisons, or the financial cost of incentives for residents to break contracts in nursing homes. In this paper, we examine how to structure these releases over time to de-densify isolated facilities under several competing objectives. We model the impact of strategic releases on infection transmission with a quadratic function that relates population size and daily interaction rate, which we call the de-densification function. Then, we formulate the decision problem as a multi-criteria MDP and develop dynamic solution methods that employ Monte Carlo simulations, $k$-means clustering, and $Q$ learning with linear function approximation. We consider a 100-person facility experiencing an outbreak described by a Susceptible-Infectious-Recovered epidemiological model. Under this framework, we derive theoretical conditions for the de-densification function, to ensure it has an intuitive impact on infection transmission. We also test our dynamic solution methods under a number of parameter settings, and demonstrate that our cluster-based method outperforms a static benchmark by up to 13.3% under three different de-densification functions and two priority weights. Dynamic release policies can improve long-term cost over single, one-time release actions. The use of $k$-means clustering in Monte Carlo simulations can improve objective performance while maintaining similar computational time.

Keywords: Markov Decision Processes (MDPs), epidemiological modeling, sequential decision making, uncertainty quantification (UQ), multi-objective optimization