  One of the cornerstones in combating the HIV pandemic is being able to assess
the current state and evolution of local HIV epidemics. This remains a complex
problem, as many HIV infected individuals remain unaware of their infection
status, leading to parts of HIV epidemics being undiagnosed and under-reported.
To that end, we firstly present a method to learn epidemiological parameters
from phylogenetic trees, using approximate Bayesian computation (ABC). The
epidemiological parameters learned as a result of applying ABC are subsequently
used in epidemiological models that aim to simulate a specific epidemic.
Secondly, we continue by describing the development of a tree statistic, rooted
in coalescent theory, which we use to relate epidemiological parameters to a
phylogenetic tree, by using the simulated epidemics. We show that the presented
tree statistic enables differentiation of epidemiological parameters, while
only relying on phylogenetic trees, thus enabling the construction of new
methods to ascertain the epidemiological state of an HIV epidemic. By using
genetic data to infer epidemic sizes, we expect to enhance understanding of the
portions of the infected population in which diagnosis rates are low.
