Dongni Zhang: Network epidemic models with instantaneous digital contact tracing (CT) and manual CT allowing delay

Abstract

We consider an SEIR epidemic spreading on a configuration model network but also allowing random contacts. Each infective remains infectious for a constant period. Further, we assume that such an infective is diagnosed and interviewed with some probability otherwise, we say that the infective recovers naturally. We define manual contact tracing (CT) by that once diagnosed, each of her/his infectee neighbours (manual CT is forward, only on the network) is reported with some probability independently. If such reported neighbours are infectious after some delay, they are isolated and said to be traced, so stop spreading. As for digital CT, a fraction of people use a tracing app. If the diagnosed person is also an app-user, all of her/his app-using contacts are immediately traced (digital CT both on the network and among global contacts). For both manual and digital CT, only the diagnosed individuals can trigger CT (non-iterative).    Assuming a large population, we approximate the early phases of the epidemic with manual, digital CT, and both CT, by different multi-type branching processes. The corresponding effective reproduction numbers are derived. It seems that the underlying combined model is pessimistic by only having one-step CT and even introducing a delay for manual CT, whereas our earlier model is over-optimistic by assuming iterative CT without any delay. And the real world should lie somewhere in between. This talk is based on joint work with my supervisor, Tom Britton.