Istvan Kiss: Epidemic threshold in pairwise models for clustered networks: closures and fast correlations

Abstract: The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics the epidemic threshold is well studied and understood. However, this is less so for clustered networks where there are a limited number of theoretical results. In this paper we focus on a class of models know as pairwise models where, to our knowledge, no analytical results for the epidemic threshold exist. We show that exploiting the presence of fast variables and using some standard techniques from perturbation theory we are able to obtain the growth-rate-based epidemic threshold analytically. More precisely, this is obtained as an asymptotic expansion in terms of powers of the clustering coefficient. We compute the threshold for two different pairwise models based on two different closures and validate the threshold by comparing it to the numerical solution of the full system. The agreement is found to be excellent over a wide range of values of the clustering coefficient, transmission rate and average degree of the network.

OBS: This is a different time schedule from the usual Wednesday Mat-stat seminar.