  Genomic surveillance of infectious diseases allows monitoring circulating and
emerging variants and quantifying their epidemic potential. However, due to the
high costs associated with genomic sequencing, only a limited number of samples
can be analysed. Thus, it is critical to understand how sampling impacts the
information generated. Here, we combine a compartmental model for the spread of
COVID-19 (distinguishing several SARS-CoV-2 variants) with different sampling
strategies to assess their impact on genomic surveillance. In particular, we
compare adaptive sampling, i.e., dynamically reallocating resources between
screening at points of entry and inside communities, and constant sampling,
i.e., assigning fixed resources to the two locations. We show that adaptive
sampling uncovers new variants up to five weeks earlier than constant sampling,
significantly reducing detection delays and estimation errors. This advantage
is most prominent at low sequencing rates. Although increasing the sequencing
rate has a similar effect, the marginal benefits of doing so may not always
justify the associated costs. Consequently, it is convenient for countries with
comparatively few resources to operate at lower sequencing rates, thereby
profiting the most from adaptive sampling. Finally, our methodology can be
readily adapted to study undersampling in other dynamical systems.
