Mathematical modelling of infectious diseases involves a series of mathematical techniques and methods that make it possible to describe the dynamics of their transmission in populations. The incorporation of biological and epidemiological events related to these diseases into models, taking into account their intrinsic uncertainty, is essential to explain and predict their dynamics. This seminar introduces dynamic modelling and calibration techniques with uncertainty in two areas of epidemiology on real-world case studies: antibiotic resistance, specifically in the case study of colistin-resistant Acinetobacter baumannii, and vaccination strategies, in particular against influenza and human papillomavirus (HPV). Combining deterministic and stochastic mathematical modelling techniques, parameter analysis and calibration strategies, we can explain the observed epidemiological scenarios, predict their evolution and evaluate the efficacy of preventive public health interventions.