Disease Progression on Social Networks

The deterministic SIR and SIS models are generally accepted as an efficient way to represent the theoretical number of people in a population infected by a disease over a certain period of time. The goal of this study was to find another method of representing these outbreaks, specifically a stochastic model. To find a stochastic alternative to the SIR and SIS models, graph population and node states were observed as simulators of disease on four different graph types; random, scale-free, configuration model, and hierarchical configuration model. Each node on the graph represented a person and each edge between two nodes represented an interaction between two people. A disease was then introduced into the population and the spread simulated. Once completed, a plot of data was constructed comparing the evolution of the number of susceptible, infected and recovered or dead nodes versus time. This stochastic model was then compared to the deterministic SIR and SIS models, and was found to be a viable alternative on each of the four graph types. Data for an outbreak of Dengue in Puerto Rico was then compared the the stochastic SIR model that had been tested. This data was also used to compare how each of the four graph types compared to real world disease spread data.