Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks

• Published in: Physical review letters Vol. 117; no. 22; p. 228302
• Main Authors: Zino, Lorenzo, Rizzo, Alessandro, Porfiri, Maurizio
• Format: Journal Article
• Language: English
• Published: United States 25-11-2016
• Subjects: Computer simulation; Dynamical systems; Epidemics; Mathematical analysis; Mathematical models; Networks; Spreading; Time
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/physrevlett.117.228302

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.