The study of epidemiology, evolutionary biology and immunology are well-developed fields in their own right. However, current problems in disease dynamics have arisen that cross these disciplinary boundaries and where stochastic modeling and methods are essential to progress in these fields. Stochasticity plays an important role in the study of emergence of new diseases, pathogen evolution in response to control strategies or therapies, chance interactions of multiple species or multiple pathogens, variability in the host immune response, and disease propagation locally and globally. Tools from branching processes, percolation theory and network theory have demonstrated the importance of connectivity and cluster size in disease spread. The study of stochastic epidemic models has provided information about the duration and final size distributions, the probability of pathogen extinction or persistence and the quasistationary distribution. The availability of increasing amounts of data on within-host pathogens and on recent epidemics and the increase in computational power allow more accurate predictions of future trends and enable model predictions to be statistically tested and the uncertainty quantified. New mathematical, statistical and computational approaches for discrete- and continuous-time processes are needed to realistically model, analyze, compute and test the within-host and the between-host variability in response to a pathogen invasion and to connect the large-scale stochastic spatial epidemic or pandemic models to the small-scale within-host pathogen dynamics. Through collaboration among mathematicians, statisticians and applied scientists, important interdisciplinary problems in epidemiology, immunology and evolutionary biology can be addressed which will involve challenges in model development, statistical analysis, and computational methodology.