Epidemic Propagation Dynamics on Complex Networks

This paper provides a partial summary of our recent work on propagation dynamics of complex networks, mainly on constructing and studying network models of disease spreading and related propagation problems. Traditional compartmen-tal models of disease spreading categorize individuals from a population based on their current pathology. These methods provide a population-based description that offers a smooth continuous and exponential response to the presence of an infectious agent. In many cases the available data is inconsistent with the standard models of disease spreading and can be more readily explained using a discrete agent-based model of spreading on complex networks. Moreover, models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. In addition, some diseases may develop through several stages, or with mobility property, or with mutually exclusive feature (multi-strain epidemics). So in this paper, in order to better study the dynamical behavior of epidemics, we discuss different epidemic models on complex networks, and provide a mathematical analysis of the epidemic dynamics and spreading behavior, obtaining the epidemic threshold for each case. Some other related diffusion and propagation processes, such as information transmission dynamics, traffic flows, contact processes, etc., are also briefly discussed. © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.