Complex immunological interactions between multiple strains of disease, such as short-term immunity or cross-protection, govern the evolutionary and epidemiological dynamics of disease. Understanding these interactions plays a vital role in clinical and public health decision-making and advances our understanding of the mechanisms of disease transmission and progression at the individual and population levels. This project aims to develop and fit (1) a three-pathogen interaction model to influenza A, influenza B, and RSV surveillance data and (2) a four-pathogen interaction model to dengue surveillance data to estimate the duration and strength of cross-protection and enhancement between these pathogens and between the four serotypes of dengue. We are also developing and implementing a statistical framework for comparing inferences from mechanistic and phenomenological models of multiple interacting time series. This work will provide the first explicit estimates of cross-protection between influenza A, influenza B, and RSV, and the first explicit estimates of immune enhancement between the four serotypes of dengue. Methods developed in the course of this work will be freely disseminated as R software packages (more info to come).