  This study proposes a nonhomogeneous birth--death model which captures the
dynamics of a directly transmitted infectious disease. Our model accounts for
an important aspect of observed epidemic data in which only symptomatic
infecteds are observed. The nonhomogeneous birth--death process depends on
survival distributions of reproduction and removal, which jointly yield an
estimate of the effective reproduction number $R(t)$ as a function of epidemic
time. We employ the Burr distribution family for the survival functions and, as
special cases, proportional rate and accelerated event-time models are also
employed for the parameter estimation procedure. As an example, our model is
applied to an outbreak of avian influenza (H7N7) in the Netherlands, 2003,
confirming that the conditional estimate of $R(t)$ declined below unity for the
first time on day 23 since the detection of the index case.
