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LoRaWAN is a promising low power long range wireless communications technology for the Internet of Things. An important feature of LoRaWAN gateways is related to so-called capture effect: under some conditions the gateway may correctly receive a frame even if it overlaps with other ones. In this paper, we develop a pioneering mathematical model of a LoRaWAN network which allows finding network capacity and transmission reliability taking into account the capture effect.