(eng): Background:\nContact tracing is one of the most effective non-pharmaceutical interventions in the COVID-19 pandemic. This study uses a multi-agent model to investigate the impact of four types of contact tracing strategies to prevent the spread of COVID-19.\nMethods:\nIn order to analyse individual contact tracing in a reasonably realistic setup, we construct an agent-based model of a small municipality with about 60.000 inhabitants (nodes) and about 2.8 million social contacts (edges) in 30 different layers. Those layers reflect demographic, geographic, sociological and other patterns of the TTWA (Travel-to-work-area) Hodonín in Czechia. Various data sources such as census, land register, transport data or data reflecting the shopping behaviour, were employed to meet this purpose. On this multi-graph structure we run a modified SEIR model of the COVID-19 dynamics. The parameters of the model are calibrated on data from the outbreak in the Czech Republic in the period March to June 2020. The simplest type of contact tracing follows just the family, the second tracing version tracks the family and all the work contacts, the third type finds all contacts with the family, work contacts and friends (leisure activities). The last one is a complete (digital) tracing capable of recalling any and all contacts.\nWe evaluate the performance of these contact tracing strategies in four different environments. First, we consider an environment without any contact restrictions (benchmark), second with strict contact restriction (replicating the stringent non-pharmaceutical interventions employed in Czechia in the spring 2020), third environment, where the measures were substantially relaxed, and, finally an environment with weak contact restrictions and superspreader events (replicating the situation in Czechia in the summer 2020).\nFindings:\nThere are four main findings in our paper. 1. In general, local closures are more effective than any type of tracing. 2. In an environment with strict contact restrictions there are only small differences among the four contact tracing strategies. 3. In an environment with relaxed contact restrictions the effectiveness of the tracing strategies differs substantially. 4. In the presence of superspreader events only complete contact tracing can stop the epidemic.