Tracing and testing the COVID-19 contact chain: cost-benefit tradeoffs

Traditional contact tracing for COVID-19 tests the direct contacts of those who test positive even if the contacts do not show any symptom. But, why should the testing stop at direct contacts, and not test secondary, tertiary contacts or even contacts further down? The question arises because by the time an infected individual is tested the infection starting from him may have infected a chain of individuals. 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 testing the contact chain of an individual who tests positive. For this investigation, we utilize multiple human contact networks, spanning two real-world data sets of spatio-temporal records of human presence over certain periods of time, as also networks of a classical synthetic variety. Over the diverse set of contact patterns, we discover that testing the contact chain can both substantially reduce over time both the cumulative infection count and the testing load. We consider elements of human behavior that enhance the spread of the disease and lower the efficacy of testing strategies, and show that testing the contact chain enhances the resilience to adverse impacts of these elements. We also discover a phenomenon of diminishing return beyond a threshold value on the depth of the chain to be tested in one go, the threshold then provides the most desirable tradeoff between benefit in terms of reducing the cumulative infection count, enhancing resilience to adverse impacts of human behavior, and cost in terms of increasing the testing load.