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"The final publication is available at Springer via http://dx.doi.org/10.1007/s10588-013-9156-z ; We present a new mathematical model that predicts the number of users informed and influenced by messages that are propagated in an online social network. Our model is based on a new way of quantifying the tie-strength, which in turn considers the affinity and relevance between nodes. We could verify that the messages to inform and influence, as well as their importance, produce different propagation behaviors in an online social network. We carried out laboratory tests with our model and with the baseline models Linear Threshold and Independent Cascade, which are currently used in many scientific works. The results were evaluated by comparing them with empirical data. The tests show conclusively that the predictions of our model are notably more accurate and precise than the predictions of the baseline models. Our model can contribute to the development of models that maximize the propagation of messages; to predict the spread of viruses in computer networks, mobile telephony and online social networks. ; This work was carried out by the financing of the Ecuadorian government of President Rafael Correa D. and by FLAMINGO, a Network of Excellence project (318488) supported by the European Commission under the Seventh Framework Program and the project TEC2015-71329-C2-2-R (MINECO/FEDER) from Ministerio de Economía y Competitividad. R.M.O-G. thanks Dr. Joan Serrat Fernández, Dr. Xavier Muñoz and Dr. Josep Fàbrega, professors at the University Polytechnic of Catalonia. Similarly, Dr. Esteban Samaniego Alvarado and PhD student Vladimiro Tobar Solano, professors at Universidad de Cuenca, and the PhD student Lucía Mendez Tapia for the accomplishment of this work. ; Peer Reviewed ; Postprint (author's final draft)