Mathematical models of infectious disease spread can be used to study both recurrent and emergent epidemics. Here, we explore both contexts. The first two chapters focus on modeling seasonal mechanisms in recurrent infectious diseases. We investigate the repercussions of using different models of seasonal forcing in childhood infectious disease dynamics and find a surprising invariance in long-term model behaviour. In another project, we propose a simple model of repeated individual vaccination decisions motivated by annual seasonal influenza vaccination campaigns. The second part of this dissertation adds to our understanding of modeling an emerging pandemic disease: COVID-19. We study age-based heterogeneities in COVID-19 severity in order to inform models of COVID-19-related hospitalizations, ICU admissions, and deaths. We also develop several crucial extensions to a COVID-19 model that have enabled the continued production of accurate and useful forecasts through the current phase of the pandemic, where vaccination efforts race emerging viral variants.