doi:10.1515/fca-2020-0033engAbadias, LEstrada-Rodriguez, GEstrada, EFractional-order susceptible-infected model: definition and applications to the study of covid-19 main proteaseART-2020-118940We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics consists of a Susceptible-Infected (SI) model based on the Caputo fractional-order derivative. We find an upper bound to the analytical solution of this model which represents the worse-case scenario on the propagation of perturbations across a protein residue network. This upper bound is expressed in terms of Mittag-Leffler functions of the adjacency matrix of the network of inter-amino acids interactions. We then apply this model to the analysis of the propagation of perturbations produced by inhibitors of the main protease of SARS CoV-2. We find that the perturbations produced by strong inhibitors of the protease are propagated far away from the binding site, confirming the long-range nature of intra-protein communication. On the contrary, the weakest inhibitors only transmit their perturbations across a close environment around the binding site. These findings may help to the design of drug candidates against this new coronavirus.2020http://zaguan.unizar.es/record/13078510.1515/fca-2020-0033http://zaguan.unizar.es/record/130785oai:zaguan.unizar.es:130785info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MCYTS-MTM2016-77710-PFractional Calculus and Applied Analysis 23, 3 (2020), 635-655by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess