title: An individual-based approach to SIR epidemics in contact networks.
abstract: Many approaches have recently been proposed to model the spread of epidemics on networks. For instance, the Susceptible/Infected/Recovered (SIR) compartmental model has successfully been applied to different types of diseases that spread out among humans and animals. When this model is applied on a contact network, the centrality characteristics of the network plays an important role in the spreading process. However, current approaches only consider an aggregate representation of the network structure, which can result in inaccurate analysis. In this paper, we propose a new individual-based SIR approach, which considers the whole description of the network structure. The individual-based approach is built on a continuous time Markov chain, and it is capable of evaluating the state probability for every individual in the network. Through mathematical analysis, we rigorously confirm the existence of an epidemic threshold below which an epidemic does not propagate in the network. We also show that the epidemic threshold is inversely proportional to the maximum eigenvalue of the network. Additionally, we study the role of the whole spectrum of the network, and determine the relationship between the maximum number of infected individuals and the set of eigenvalues and eigenvectors. To validate our approach, we analytically study the deviation with respect to the continuous time Markov chain model, and we show that the new approach is accurate for a large range of infection strength. Furthermore, we compare the new approach with the well-known heterogeneous mean field approach in the literature. Ultimately, we support our theoretical results through extensive numerical evaluations and Monte Carlo simulations.
authors.affiliation: K-State Epicenter: Center for Complex Network Approach to EpiModeling, Department of Electrical and Computer Engineering, Kansas State University, 2061 Rathbone Hall, Manhattan, KS 66506, USA. mkamel@ksu.edu
authors.forename: Mina
authors.initials: M
authors.lastname: Youssef
authors.forename: Caterina
authors.initials: C
authors.lastname: Scoglio
mesh_terms: D000818:Animals; D004198:Disease Susceptibility; D018562:Disease Transmission, Infectious; D058872:Epidemics; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method