  Contact tracing has been extensively studied from different perspectives in
recent years. However, there is no clear indication of why this intervention
has proven effective in some epidemics (SARS) and mostly ineffective in some
others (COVID-19). Here, we perform an exhaustive evaluation of random testing
and contact tracing on novel superspreading random networks to try to identify
which epidemics are more containable with such measures. We also explore the
suitability of positive rates as a proxy of the actual infection statuses of
the population. Moreover, we propose novel ideal strategies to explore the
potential limits of both testing and tracing strategies. Our study counsels
caution, both at assuming epidemic containment and at inferring the actual
epidemic progress, with current testing or tracing strategies. However, it also
brings a ray of light for the future, with the promise of the potential of
novel testing strategies that can achieve great effectiveness.
