TIME-VARYING SIS PREVALENCE IN NETWORKS: THEORY AND A NEW APPROXIMATE
FORMULA
25 febbraio 2016
*Luogo:* Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula
Seminari
*Ore* 10:00
*Relatore:*
- *Piet Van Mieghem** (*TU Delft Olanda*)*
*Abstract: *
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