Recently, the use of air base stations located on unmanned aerial vehicles (UAVs) has attracted great attention. Static deployment of a sufficient number of UAVs allows uniform wireless coverage in the demanded areas, where the existing cellular infrastructure has white spots or insufficient capacity. However, UAVs mobility may be required for applications, where UAVs are used to provide communications for mobile groups of users (e.g., massive sport or community events like marathon or music festival) or for patrolling tasks with relaxed requirements for data transmission delays (for example, when collecting information from a large number of mMTC sensors). In such tasks, the movement of UAVs can significantly increase the efficiency of the system, since in this case the coverage of the area can be provided by a smaller number of UAVs following the dynamics of ground users. Nowadays, more and more often the question arises about the mobile communications availability in a remote area, for example, during public events or search operations. The lack of on-demand connectivity with sufficient quality in such areas is unacceptable in modern conditions. Therefore, the study of the behavior of a dynamic UAV network is necessary for decision-making operation in such scenarios. The main contribution of this work is making the user mobility model more human-alike according to the real scenarios. The paper considers two models of UAVs movement, the effectiveness of which is estimated from the point of view of the coverage probability and average fade duration of the signal. © 2020, Springer Nature Switzerland AG.