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Efficient contact tracing and isolation is an effective strategy to controlepidemics. It was used effectively during the Ebola epidemic and successfullyimplemented in several parts of the world during the ongoing COVID-19 pandemic.An important consideration in contact tracing is the budget on the number ofindividuals asked to quarantine -- the budget is limited for socioeconomicreasons. In this paper, we present a Markov Decision Process (MDP) framework toformulate the problem of using contact tracing to reduce the size of anoutbreak while asking a limited number of people to quarantine. We formulateeach step of the MDP as a combinatorial problem, MinExposed, which wedemonstrate is NP-Hard; as a result, we develop an LP-based approximationalgorithm. Though this algorithm directly solves MinExposed, it is oftenimpractical in the real world due to information constraints. To this end, wedevelop a greedy approach based on insights from the analysis of the previousalgorithm, which we show is more interpretable. A key feature of the greedyalgorithm is that it does not need complete information of the underlyingsocial contact network. This makes the heuristic implementable in practice andis an important consideration. Finally, we carry out experiments on simulationsof the MDP run on real-world networks, and show how the algorithms can help inbending the epidemic curve while limiting the number of isolated individuals.Our experimental results demonstrate that the greedy algorithm and its variantsare especially effective, robust, and practical in a variety of realisticscenarios, such as when the contact graph and specific transmissionprobabilities are not known. All code can be found in our GitHub repository:https://github.com/gzli929/ContactTracing.

A Markov Decision Process Framework for Efficient and Implementable Contact Tracing and Isolation