Currently, the wireless body area network for monitoring the human body and preventing the critical situations of life are widely spread. Data from the sensors are collected in the memory of the microcomputer, and should be delivered in a cloud service for the further analysis. The classical methods for delivery via wireless interfaces require large power consumption (Wifi, LTE, 3G technology), whereas the protocols with low power consumption suggest the presence of additional gateway with the Internet, which is not always possible to implement. The paper proposes an original approach of using UAVs to deliver data from the wireless body area network to a remote cloud server. The proposed model takes into account the bandwidth, the ability of generating traffic parameters, the number of sensor nodes and the characteristics of the UAV.