Contact Tracing and Stochastic Graphs

Contact tracing is a quite interesting method to fight infectious diseases: if an infected person is discovered, this person is asked about the (potentially) infectious contacts. The corresponding individuals are then examined, and in this way it is possible to find further infected persons.

Though the common belief and the common feeling is that this measure to fight diseases is quite effective (also with monetary aspects in mind). However, there are almost no monitoring structures or possible to derive an objective idea about the efficacy of contact tracing.

We propose a (stochastic, individual-based) model for contact tracing. The central aspect of this model is the graph that is generated by infected persons: the nodes are the infected persons, a directed edge goes from infector to infectee. Contact tracing takes place along the edges of this graph. First, we derive (in an heuristic way) an ordinary differential equation. Then, we derive results about the structure of the stochastic graph. In an outlook, we try to sketch ideas how to use these models to set up monitoring tools using these results.