Path-Based Epidemic Spreading in Networks

Conventional epidemic models assume omni-directional contact-based infection. This strongly associates the epidemic spreading process with node degrees. The role of the infection transmission medium is often neglected. In real-world networks, however, the infectious agent as the physical contagion medium usually flows from one node to another via specific directed routes (path-based infection). Here, we use continuous-time Markov chain analysis to model the influence of the infectious agent and routing paths on the spreading behavior by taking into account the state transitions of each node individually, rather than the mean aggregated behavior of all nodes. By applying a mean field approximation, the analysis complexity of the path-based infection mechanics is reduced from exponential to polynomial. We show that the structure of the topology plays a secondary role in determining the size of the epidemic. Instead, it is the routing algorithm and traffic intensity that determine the survivability and the steady-state of the epidemic. We define an infection characterization matrix that encodes both the routing and the traffic information. Based on this, we derive the critical path-based epidemic threshold below which the epidemic will die off, as well as conditional bounds of this threshold which network operators may use to promote/suppress path-based spreading in their networks. Finally, besides artificially generated random and scale-free graphs, we also use real-world networks and traffic, as case studies, in order to compare the behaviors of contact- and path-based epidemics. Our results further corroborate the recent empirical observations that epidemics in communication networks are highly persistent.