It seems that we are far from controlling COVID-19 pandemics, and, consequently, returning to a fully normal life. Until an effective vaccine is found, safety measures as the use of face masks, social distancing, washing hands regularly, etc., have to be taken. Also, the use of appropriate antivirals in order to alleviate the symptoms, to control the severity of the illness and to prevent the transmission, could be a good option that we study in this work. In this paper, we propose a computational random network model to study the transmission dynamics of COVID-19 in Spain. Once the model has been calibrated and validated, we use it to simulate several scenarios where effective antivirals are available. The results show how the early use of antivirals may significantly reduce the incidence of COVID-19 and may avoid a new collapse of the health system. (c) 2020 Elsevier Ltd. All rights reserved.