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Contact tracing and quarantine are well established non-pharmaceuticalepidemic control tools. The paper aims to clarify the impact of these measuresin COVID-19 epidemic. A new deterministic model is introduced (SEIRQ:susceptible, exposed, infectious, removed, quarantined) with Q compartmentcapturing individuals and releasing them with delay. We obtain a simple ruledefining the reproduction number $\mathcal{R}$ in terms of quarantineparameters, ratio of diagnosed cases and transmission parameters. The model isapplied to the epidemic in Poland in March - April 2020, when social distancingmeasures were in place. We investigate 3 scenarios corresponding to differentratios of diagnosed cases. Our results show that depending on the scenariocontact tracing could have prevented from 50\% to over 90\% of cases. Theeffects of quarantine are limited by fraction of undiagnosed cases. Taking intoaccount the transmission intensity in Poland prior to introduction of socialrestrictions it is unlikely that the control of the epidemic could be achievedwithout any social distancing measures.

A new SEIR type model including quarantine effects and its application to analysis of Covid-19 pandemia in Poland in March-April 2020