SIR and SIS Epidemic Dynamics in Random Contact Networks

In this paper is discussed the mathematical formalization of probabilistic procedures for the SIR and SIS infectious diseases epidemic models, over Erdös-Rényi contact networks. The epidemic threshold is defined by the inverse of the spectral radius of the associated adjacency matrices, which expresses the network topology and its global dynamics. Several numerical case studies are performed, according to different choices of the seed set, considering random or chosen seeds within the centrality measures: degree, closeness, betweenness and eigenvalue. This numerical study analyzes different perspectives of the local and global dynamics of the contact networks under study.