Ebola Impact and Quarantine in a Network Model

Abstract

Much effort has been directed towards using mathematical models to understand and predict contagious disease, in particular Ebola outbreaks. Classical SIR (susceptible-infected-recovered) compartmental models capture well the dynamics of the outbreak in certain communities, and accurately describe the differences between them based on a variety of parameters. However, repeated resurgence of Ebola contagions suggests that there are components of the global disease dynamics that we don’t yet fully understand and can’t effectively control. In order to understand the dynamics of a more widespread contagion, we placed SIR models within the framework of dynamic networks, with the communities at risk of contracting the virus acting as nonlinear systems, coupled based on a connectivity graph. We study how the effects of the disease (measured as the outbreak impact and duration) change with respect to local parameters, but also with changes in both short-range and long-range connectivity patterns in the graph. We discuss the implications of optimizing both these measures in increasingly realistic models of coupled communities. KEYWORDS: Epidemic Spread; Network Dynamics; Network Connectivity; Coupled Differential Equations; Compartmental Model; Information Transfer; Outbreak Impact; Outbreak Duration