State discretization for continuous-state MDPs in infectious disease control

Abstract

Repeated decision-making problems may arise in the health policy context, such as infectious disease control for COVID-19 and other epidemics. These problems may sometimes be effectively solved using Markov decision processes (MDPs). However, the continuous or large state space of such problems for capturing infectious disease prevalence renders it difficult to implement tractable MDPs to identify the optimal disease control policy over time. We therefore develop an algorithm for discretizing continuous states for approximate MDP solutions in this context. We benchmark performance against a uniform discretization using both a synthetic example and an example of COVID-19 in Los Angeles County.