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  1. 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. 
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