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Determining COVID-19 vaccination strategies presents many challenges in light of limited vaccination capacity and the heterogeneity of affected communities. Who should be prioritized for early vaccination when different groups manifest different levels of risks and contact rates? Answering such questions often becomes computationally intractable given that network size can exceed millions. We obtain a framework to compute the optimal vaccination strategy within seconds to minutes from among all strategies, including highly dynamic ones that adjust vaccine allocation as often as required, and even with modest computation resources. We then determine the optimal strategy for a large range of parameter values representative of various US states, countries, and case studies including retirement homes and prisons. The optimal is almost always one of a few candidate strategies, and, even when not, the suboptimality of the best among these candidates is minimal. Further, we find that many commonly deployed vaccination strategies, such as vaccinating the high risk group first, or administering second doses without delay, can often incur higher death rates, hospitalizations, and symptomatic infection counts. Our framework can be easily adapted to future variants or pandemics through appropriate choice of the compartments of the disease and parameters. 

A preemptive multi-hop contact tracing scheme that tracks not only the direct contacts of those who tested positive for COVID-19, but also secondary or tertiary contacts has been proposed and deployed in practice with some success. We propose a mathematical methodology for evaluating this preemptive contact tracing strategy that combines the contact tracing dynamics and the virus transmission mechanism in a single framework using microscopic Markov Chain approach (MMCA). We perform Monte Carlo (MC) simulations to validate our model and show that the output of our model provides a reasonable match with the result of MC simulations. Utilizing the formulation under a human contact network generated from real-world data, we show that the cost-benefit tradeoff can be significantly enhanced through an implementation of the multi-hop contact tracing as compared to traditional contact tracing. We further shed light on the mechanisms behind the effectiveness of the multi-hop testing strategy using the framework. We show that our mathematical framework allows significantly faster computation of key attributes for multi-hop contact tracing as compared to MC simulations. This in turn enables the investigation of these attributes for large contact networks, and constitutes a significant strength of our approach as the contact networks that arise in practice are typically large. 

Traditional contact tracing tests the direct contacts of those who test positive. But, by the time an infected individual is tested, the infection starting from the person may have infected a chain of individuals. Hence, why should the testing stop at direct contacts, and not test secondary, tertiary contacts or even contacts further down? One deterrent in testing long chains of individuals right away may be that it substantially increases the testing load, or does it? We investigate the costs and benefits of such multi-hop contact tracing for different number of hops. Considering diverse contact networks, we show that the cost–benefit trade-off can be characterized in terms of a single measurable attribute, the initial epidemic growth rate . Once this growth rate crosses a threshold, multi-hop contact tracing substantially reduces the outbreak size compared with traditional tracing. Multi-hop even incurs a lower cost compared with the traditional tracing for a large range of values of the growth rate. The cost–benefit trade-offs can be classified into three phases depending on the value of the growth rate. The need for choosing a larger number of hops becomes greater as the growth rate increases or the environment becomes less conducive toward containing the disease.