The costs of overcrowding (and release): Strategic discharges for isolated facilities during epidemiological outbreaks

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 a multi -criteria MDP and develop dynamic algorithms that employ Monte Carlo simulations, k -means clustering, and Q -learning with linear function approximation. We consider a 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. Via extensive numerical studies, we show that dynamic release policies can improve long-term cost over single, one-time release actions, and the use of k -means clustering in Monte Carlo simulations can improve objective performance while maintaining similar computational time.