![]() ![]() tracing and testing the direct, secondary and tertiary contacts of those who test positive). tracing and testing only the direct contacts of those who test positive) and 3-hop contact tracing shown on bottom (i.e. ( a) We use an example to illustrate and compare 1-hop contact tracing shown on top (i.e. And by virtue of its design, multi-hop contact tracing grows the testing cluster faster than traditional contact tracing.įigure 1. If the testing cluster grows faster than the infection cluster and also substantially overlaps with the latter, the outbreak will be contained. In this sense, contact tracing emulates the spread of the disease. Contact tracing also forms clusters of tested individuals that grow from and around one or more individuals who initially test positive ( figure 1 b). during the spread of COVID-19, large clusters were observed in meat-packing plants in seven countries, and an e-commerce distribution warehouse in South Korea. To see why multi-hop contact tracing may be effective, note that an infectious disease spreads through growth of clusters of infected individuals around one or more origins, e.g. Such multi-hop tracing and testing will enable identification and quarantine of the individuals further down the chain who have been exposed, earlier than if we had tested only the direct contacts of those who have tested positive and then reach down the chain iteratively. įewer people are likely to be infected by testing and quarantining not only direct contacts of an individual who tests positive, but contacts of the contacts and so on ( figure 1 a). A recent study suggests that, due to the high speed of transmission, the epidemic may continue to grow even if all contacts are quarantined with some delay. In the time that elapses between when an individual, i, is infected until i is tested, the disease spreads from i through a chain of several hops- i infects those i is in contact with, those whom i infects can infect their contacts, the infected contacts can infect their contacts, and so on. A question that naturally arises in this regard is if cost–benefit trade-offs may be enhanced through natural generalizations of the core concept of contact tracing-this is what we seek to answer in this paper. We also want to understand circumstances where the traditional approach is not efficient enough and how we can overcome this. In this paper, we want to understand under what circumstances traditional contact tracing alone is sufficient to contain the virus and why such containment is attainable in those circumstances. ![]() Slowing down the spread by contact tracing comes at the cost of an increase in the testing load, yet, the cost–benefit trade-off for contact tracing is understood to be substantially favourable, as compared with universal lockdowns, for example, which has led to economic downturns in several countries. Discovering and quarantining those infected contacts will stop them from spreading the disease much earlier than a strategy in which only symptomatic individuals who seek medical help are tested. This pre-emptive action, commonly known as contact tracing, is deployed because, given how contagious the disease is, a patient is likely to have passed the virus to their contacts, and the infected contacts have the potential to infect others even before they show symptoms. To slow down the spread of COVID-19, public health authorities like the US Center for Disease Control and Prevention (CDC) recommended testing those who have in the recent past been in physical proximity with an individual who has tested positive, even when the contacts do not exhibit any symptom. 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. The cost–benefit trade-offs can be classified into three phases depending on the value of the growth rate. Multi-hop even incurs a lower cost compared with the traditional tracing for a large range of values of the growth rate. Once this growth rate crosses a threshold, multi-hop contact tracing substantially reduces the outbreak size compared with traditional tracing. 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. 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. ![]() But, by the time an infected individual is tested, the infection starting from the person may have infected a chain of individuals. Traditional contact tracing tests the direct contacts of those who test positive. ![]()
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