Cope with the COVID-19 pandemic : dynamic bed allocation and patient subsidization in a public healthcare system

Abstract

In many countries and territories, public hospitals play a major role in coping with the COVID-19 pandemic. For public hospital managers, on the one hand, they must best utilize their hospital beds to serve the COVID-19 patients immediately. On the other hand, they need to consider the need of bed resources from non-COVID-19 patients, including emergency and elective patients. In this work, we consider two control mechanisms for public hospital managers to maximize the overall utility of patients. One is the dynamic allocation of bed resources according to the evolution process of the COVID-19 pandemic. The other is the usage of a subsidy scheme to move elective patients from the public to private hospitals. We develop a dynamic programming model to study the effect of bed allocation and patient subsidization in serving three types of patients, COVID-19, emergency, and elective-care. We first demonstrate the multimodularity of the total expected cost function on the number of isolation beds and the length of waiting list, which assures the monotonicity of the optimal allocation decision (i.e., how many beds should be transferred between isolation beds and ordinary beds) and the optimal subsidization decision (i.e., how many elective patients should be moved to private hospitals) in the state variables in each period. We then show that the dynamic allocation between isolation and ordinary beds can provide a better utilization of bed resources, by cutting down at least 33.5% of the total cost compared with the static policy (i.e., keeping a fixed number of isolation beds) when facing a medium pandemic alert. Furthermore, we present that subsidizing elective patients and moving them to private hospitals is an efficient way to ease the overcrowded situation in public hospitals, as we numerically show that it could reduce the length of waiting list and the total expected cost at the same time.