Modeling the impacts of contact tracing on an epidemic with asymptomatic infection

Contact tracing is widely adopted to inhibit the epidemics in the global world, and has been proved to be very effective in reducing infections. But it is rarely investigated whether contact tracing can completely eradicate an epidemic with asymptomatic infection. This paper proposes a novel model to explore the impacts of contact tracing on the outbreak size and outbreak threshold of an epidemic with asymptomatic infection in a two-layered network structure. Based on contact tracing, three types of effects are considered simultaneously: social distancing on the close contacts, infection test on the close contacts, and arousing risk perception from the close contacts. The results indicate that contact tracing and its three effects can largely reduce the number of infections. Among the three effects, the effect of social distancing is more effective because it acts on both the susceptible nodes and the asymptomatic nodes, while the other two only act on one type of nodes. However, contact tracing and its three effects are unable to change the epidemic threshold, even if the asymptomatic nodes and symptomatic nodes are all set to be infectious. The primary reason is that the identification of close contacts is driven by the detection of infections, and is lagged behind the outbreak of epidemic. In fact, the threshold for close contacts to emerge is highly dependent on the epidemic threshold. When the epidemic size approaches 0, close contacts will also disappear. To increase the efficiency of contact tracing on the epidemic threshold, the optimal strategy should directly target the normal people besides the close-contact individuals.