  The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus
occurs so rapidly that the viruses' genomes contain information on past
ecological dynamics. Hence, we develop a phylodynamic method that enables the
joint estimation of epidemiological parameters and phylogenetic history. Based
on a compartmental susceptible-infected-removed (SIR) model, this method
provides separate information on incidence and prevalence of infections.
Detailed information on the interaction of host population dynamics and
evolutionary history can inform decisions on how to contain or entirely avoid
disease outbreaks.
  We apply our Birth-Death SIR method (BDSIR) to two viral data sets. First,
five human immunodeficiency virus type 1 clusters sampled in the United Kingdom
between 1999 and 2003 are analyzed. The estimated basic reproduction ratios
range from 1.9 to 3.2 among the clusters. All clusters show a decline in the
growth rate of the local epidemic in the middle or end of the 90's.
  The analysis of a hepatitis C virus (HCV) genotype 2c data set shows that the
local epidemic in the C\'ordoban city Cruz del Eje originated around 1906
(median), coinciding with an immigration wave from Europe to central Argentina
that dates from 1880--1920. The estimated time of epidemic peak is around 1970.
