On the dynamics of interacting spreading processes

Abstract

A significant number of processes we observe in nature can be described as a spreading process; any agent which is compelled to survive by replicating through a population, examples include viruses, opinions, and information. Accordingly, a significant amount of thought power has been spent creating tools to aid in understanding spreading processes: How do they evolve? When do they thrive? What can we do to control them? Often times these questions are asked with respect to processes in isolation, when agents are free to spread to the maximum extent possible given topological and characteristic constraints. Naturally, we may be interested in considering the dynamics of multiple processes spreading through the same population, examples of which there are no shortage; we frequently characterize nature itself by the interaction and competition present at all scales of life. Recently the number of investigations into interacting processes, particularly in the context of complex networks, has increased. The roles of interaction among processes are varied from mutually beneficial to hostel, but the goals of these investigations has been to understand the role of topology in the ability of multiple processes to co-survive. A consistent feature of all present works -- within the current authors knowledge -- is that conclusions of coexistence are based on marginal descriptions population dynamics. It is the main contribution of this work to explore the hypothesis that purely marginal population descriptions are insufficient indicators of co-survival between interacting processes. Specifically, evaluating coexistence based on non-zero marginal populations is an over-simplistic definition. We randomly generate network topologies via a community based algorithm, the parameters of which allow for trivially controlling possibility of coexistence. Both marginal and conditional probabilities of each process surviving is measured by stochastic simulations. We find that positive marginal probabilities for both processes existing long term does not necessarily imply coexistence, and that marginal and conditional measurements only agree when layers are strongly anti-correlated (sufficiently distinct). In addition to the present thesis, this work is being prepared for a journal article publication. The second portion of this thesis presents numerical simulations for the Adaptive Contact - Susceptible Alert Infected Susceptible model. The dynamics of interaction between an awareness process and an infectious process are computed over a multilayer network. The rate at which nodes "switch" their immediate neighbors (contacts) when exposed to the infection is varied and numerical solutions to the epidemic threshold are computed according to mean-field approximation. We find two unexpected cases where certain parameter configurations allow the epidemic threshold to either increase above or decrease below the theoretical limits of the layers when considered individually. These computations were performed as part of a separate journal article that has been accepted for publication.