  A primary quantity of interest in the study of infectious diseases is the
average number of new infections that an infected person produces. This
so-called reproduction number has significant implications for the disease
progression. There has been increasing literature suggesting that
superspreading, the significant variability in number of new infections caused
by individuals, plays an important role in the spread of SARS-CoV-2. In this
paper, we consider the effect that such superspreading has on the estimation of
the reproduction number and subsequent estimates of future cases. Accordingly,
we employ a simple extension to models currently used in the literature to
estimate the reproduction number and present a case-study of the progression of
COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of
the reproduction number increases with superspreading and that this improves
the performance of prediction intervals. Of independent interest is the
derivation of a transparent formula that connects the extent of superspreading
to the width of credible intervals for the reproduction number. This serves as
a valuable heuristic for understanding the uncertainty surrounding diseases
with superspreading.
