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Efficient contact tracing and isolation is an effective strategy to control epidemics. It was used effectively during the Ebola epidemic and successfully implemented in several parts of the world during the ongoing COVID-19 pandemic. An important consideration in contact tracing is the budget on the number of individuals asked to quarantine -- the budget is limited for socioeconomic reasons. In this paper, we present a Markov Decision Process (MDP) framework to formulate the problem of using contact tracing to reduce the size of an outbreak while asking a limited number of people to quarantine. We formulate each step of the MDP as a combinatorial problem, MinExposed, which we demonstrate is NP-Hard; as a result, we develop an LP-based approximation algorithm. Though this algorithm directly solves MinExposed, it is often impractical in the real world due to information constraints. To this end, we develop a greedy approach based on insights from the analysis of the previous algorithm, which we show is more interpretable. A key feature of the greedy algorithm is that it does not need complete information of the underlying social contact network. This makes the heuristic implementable in practice and is an important consideration. Finally, we carry out experiments on simulations of the MDP run on real-world networks, and show how the algorithms can help in bending the epidemic curve while limiting the number of isolated individuals. Our experimental results demonstrate that the greedy algorithm and its variants are especially effective, robust, and practical in a variety of realistic scenarios, such as when the contact graph and specific transmission probabilities are not known. All code can be found in our GitHub repository: this https URL. 

ABSTRACT We study allocation of COVID-19 vaccines to individuals based on the structural properties of their underlying social contact network. Using a realistic representation of a social contact network for the Commonwealth of Virginia, we study how a limited number of vaccine doses can be strategically distributed to individuals to reduce the overall burden of the pandemic.We show that allocation of vaccines based on individuals’ degree (number of social contacts) and total social proximity time is significantly more effective than the usually used age-based allocation strategy in reducing the number of infections, hospitalizations and deaths. The overall strategy is robust even: (𝑖) if the social contacts are not estimated correctly; (𝑖𝑖) if the vaccine efficacy is lower than expected or only a single dose is given; (𝑖𝑖𝑖) if there is a delay in vaccine production and deployment; and (𝑖𝑣) whether or not non-pharmaceutical interventions continue as vaccines are deployed. For reasons of implementability, we have used degree, which is a simple structural measure and can be easily estimated using several methods, including the digital technology available today. These results are significant, especially for resource-poor countries, where vaccines are less available, have lower efficacy, and are more slowly distributed.