  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 for networks with
varying degree distribution, the number of application users and the
probability of quarantine failure. Further, we include 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 adaption rate. Finally, both strong homophily and
especially heterophily with regards to application adoption can be detrimental.
Overall, epidemics 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.
