2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/23169The spreading of an epidemic is determined by the connectiviy patterns which underlie the population. While it has been noted that a virus spreads more easily on a network in which global distances are small, it remains a great challenge to find approaches that unravel the precise role of local interconnectedness. Such topological properties enter very naturally in the framework of our two-timestep description, also providing a novel approach to tract a probabilistic system. The method is elaborated for SIS-type epidemic processes, leading to a quantitative interpretation of the role of loops up to length 4 in the onset of an epidemic.Submitted to Phys. Rev. E; 15 pages, 11 figures, 5 tablesStatistical MechanicsDisordered Systems and Neural NetworksQuantitative Methodstext