Time-varying SIS prevalence in networks: theory and a new approximate formula
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3786
dept.math [at] unitn.it
Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
- Piet Van Mieghem (TU Delft Olanda)
Currently, epidemic spreading processes on networks are popular to model diffusion phenomena in real-world networks.
After reviewing some basics about the continuous-time SIS Markov process on networks, we will focus on the prevalence, the average fraction of infected nodes in the network. Based on a recent exact differential equation containing the Laplacian matrix of the underlying graph, the time dependence of the SIS prevalence is first studied and then upper and lower bounded by a new, explicit analytic function of time.
Our new approximate formula obeys a Riccati differential equation and bears resemblence to the classical expression in epidemiology of Kermack and McKendrick (1927), but enhanced with graph specific properties, such as the algebraic connectivity, the second smallest eigenvalue of the Laplacian of the graph.
A comparison with the N-Interwined Mean-Field Approximation (NIMFA) and simulations of the exact continuous-time Markovian SIS process on a graph exhibit the accuracy and the potential of the new analytic formula.
Referente: Stefano Bonaccorsi