Mathematical Biology and Ecology Seminar
Wednesday, March 16, 2016 - 11:05am
1 hour (actually 50 minutes)
Accounting for Heterogenous Interactions in the Spread Infections, Failures, and Behaviors_ The scaled SIS (susceptible-infected-susceptible) network process that we introduced extends traditional birth-death process by accounting for heterogeneous interactions between individuals. An edge in the network represents contacts between two individuals, potentially leading to contagion of a susceptible by an infective. The inclusion of the network structure introduces combinatorial complexity, making such processes difficult to analyze. The scaled SIS process has a closed-form equilibrium distribution of the Gibbs form. The network structure and the infection and healing rates determine susceptibility to infection or failures. We study this at steady-state for three scales: 1) characterizing susceptibility of individuals, 2) characterizing susceptibility of communities, 3) characterizing susceptibility of the entire population. We show that the heterogeneity of the network structure results in some individuals being more likely to be infected than others, but not necessarily the individuals with the most number of interactions (i.e., degree). We also show that "densely connected" subgraphs are more vulnerable to infections and determine when network structures include these more vulnerable communities.