title: Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks.
abstract: Activity-driven networks are a powerful paradigm to study epidemic spreading over time-varying networks. Despite significant advances, most of the current understanding relies on discrete-time computer simulations, in which each node is assigned an activity potential from a continuous distribution. Here, we establish a continuous-time discrete-distribution framework toward an analytical treatment of the epidemic spreading, from its onset to the endemic equilibrium. In the thermodynamic limit, we derive a nonlinear dynamical system to accurately model the epidemic spreading and leverage techniques from the fields of differential inclusions and adaptive estimation to inform short- and long-term predictions. We demonstrate our framework through the analysis of two real-world case studies, exemplifying different physical phenomena and time scales.
authors.affiliation: Dipartimento di Scienze Matematiche "G. L. Lagrange," Politecnico di Torino, 10129 Torino, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Zino
authors.affiliation: Dipartimento di Automatica e Informatica, Politecnico di Torino, 10129 Torino, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Rizzo
authors.affiliation: Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, New York 11201, USA.
authors.forename: Maurizio
authors.initials: M
authors.lastname: Porfiri