The probability for infection in SIR and SIS networks

Abstract

When we inspect a disease, the social structure may be important for how a disease spread. The people with many friends, may face a bigger risk for infection than a person with few friends. The social network we may represent by a graph, where the vertices represents persons, and the edges represents vertices. We will in this thesis use two epidemic models for how the infection propegate: The SIR network and the SIS network. In this thesis we will show three properties for the models. The monotonicity properties, the epidemic threshold and computing the probabilites are #P-hard. Also, we will describe two algorithm for computing the probabilities: an exact algorithm and a Monte-Carlo algorithm.