  Contact tracing and quarantine are well established non-pharmaceutical
epidemic control tools. The paper aims to clarify the impact of these measures
in COVID-19 epidemic. A new deterministic model is introduced (SEIRQ:
susceptible, exposed, infectious, removed, quarantined) with Q compartment
capturing individuals and releasing them with delay. We obtain a simple rule
defining the reproduction number $\mathcal{R}$ in terms of quarantine
parameters, ratio of diagnosed cases and transmission parameters. The model is
applied to the epidemic in Poland in March - April 2020, when social distancing
measures were in place. We investigate 3 scenarios corresponding to different
ratios of diagnosed cases. Our results show that depending on the scenario
contact tracing could have prevented from 50\% to over 90\% of cases. The
effects of quarantine are limited by fraction of undiagnosed cases. Taking into
account the transmission intensity in Poland prior to introduction of social
restrictions it is unlikely that the control of the epidemic could be achieved
without any social distancing measures.
