Statistical inference algorithms for epidemic processes on complex networks : : doctoral thesis - Antulov-Fantulin, Nino (N. Antulov-Fantulin ; Fakultet elektrotehnike i računarstva, 2015)
ABSTRACT: The main topics of this dissertation are novel methods and algorithms for the modelling and the statistical inference about epidemic processes based on the Susceptible-Infected-Recovered (SIR) model on arbitrary network structures. Two types of problems are solved: (i) estimation of the final epidemic outcome ("forward in time" statistical estimate) and (ii) estimation of epidemic initial conditions from a single epidemic realization ("backward in time" statistical inference). In order to estimate the final epidemic outcome on arbitrary networks without following the temporal dynamics, a novel FastSIR algorithm is constructed. The FastSIR algorithm is using a probability distribution of the number of infected nodes in a first neighbourhood in a limit of time to speed up the simulation. In the backward statistical inference, we solve two problems: (a) the detection of a single epidemic source from a realization and (b) the recognition that a realization has multiple initial sources. A number of different statistical estimators are presented for determining the likelihood for potential source producing the observed epidemic realization. The estimates are based on the Monte Carlo simulations of an epidemic spreading process on a network from a set of potential source candidates, which were infected in the observed realization. This statistical inference framework is applicable to arbitrary networks and different dynamical spreading processes. The problem of multiple-source epidemic recognition from a single realization is solved by constructing a statistical outlier detection algorithm, which is based on the Kolmogorov-Smirnov statistics over realization similarity distributions. -