  Contact tracing via digital tracking applications installed on mobile phones
is an important tool for controlling epidemic spreading. Its effectivity can be
quantified by modifying the standard methodology for analyzing percolation and
connectivity of contact networks. We apply this framework to networks with
varying degree distributions, numbers of application users, and probabilities
of quarantine failures. Further, we study structured populations with homophily
and heterophily and the possibility of degree-targeted application
distribution. Our results are based on a combination of explicit simulations
and mean-field analysis. They indicate that there can be major differences in
the epidemic size and epidemic probabilities which are equivalent in the normal
SIR processes. Further, degree heterogeneity is seen to be especially important
for the epidemic threshold but not as much for the epidemic size. The
probability that tracing leads to quarantines is not as important as the
application adoption rate. Finally, both strong homophily and especially
heterophily with regard to application adoption can be detrimental. Overall,
epidemic dynamics are very sensitive to all of the parameter values we tested
out, which makes the problem of estimating the effect of digital contact
tracing an inherently multidimensional problem.
