Epidemics have long been studied in the realm of mathematical modeling, aiding in parameter estimation, determining effective intervention methods, and, in some cases, predicting epidemics. How do networks and network structure influence infectious diseases? Are certain networks better suited to naturally contain an epidemic where others are not? In this paper, we will explore one method of stochastic modeling and implement it into a network of sub-populations. We will conclude with interesting results on networks and their dynamics in disease propagation.