Background: Our understanding of pathogens and disease transmission has improved dramatically over the past 100 years, but coinfection, how different pathogens interact with each other, remains a challenge. Cross-sectional serological studies including multiple pathogens offer a crucial insight into this problem. Methods: We use data from three cross-sectional serological surveys (in 2003, 2007 and 2013) in a Baltimore emergency department to predict the prevalence for HIV, hepatitis C virus (HCV) and herpes simplex virus, type 2 (HSV2), in a fourth survey (in 2016). We develop a mathematical model to make this prediction and to estimate the incidence of infection and coinfection in each age and ethnic group in each year. Results: Overall we find a much stronger age cohort effect than a time effect, so that, while incidence at a given age may decrease over time, individuals born at similar times experience a more constant force of infection over time. Conclusions: These results emphasise the importance of age-cohort counselling and early intervention while people are young. Our approach adds value to data such as these by providing age- and time-specific incidence estimates which could not be obtained any other way, and allows forecasting to enable future public health planning.