We develop phylodynamics models and methods to study viral epidemics, in particular HIV. This new, trendy domain is in between usual mathematical epidemiology, typically based on compartment models, and phylogenetics. The models used in phylodynamics share the common assumption that new cases are detected randomly. However, a key counter-example is given by partner notification (PN), one of the most widely used control measure against sexually transmitted infections. Our goal is to assess and model the public health impact of PN on HIV epidemics, and study possible observation biases induced by PN. Phylodynamics models are usually complex and writing down the likelihood of the data is often impossible. Thus, we develop approximate Bayesian computation (ABC) methods, which we apply to several data sets and questions (e.g. Ebola). This project is partly funded by a joint project with the Institute of Tropical Medicine “Pedro Kouri”, Havana, Cuba.