  Epidemic models often reflect characteristic features of infectious spreading
processes by coupled non-linear differential equations considering different
states of health (such as Susceptible, Infected, or Recovered). This
compartmental modeling approach, however, delivers an incomplete picture of the
dynamics of epidemics, as it neglects stochastic and network effects, and also
the role of the measurement process, on which the estimation of epidemiological
parameters and incidence values relies. In order to study the related issues,
we extend established epidemiological spreading models with a model of the
measurement (i.e. testing) process, considering the problems of false positives
and false negatives as well as biased sampling. Studying a model-generated
ground truth in conjunction with simulated observation processes (virtual
measurements) allows one to gain insights into the limitations of purely
data-driven methods to assess the epidemic situation. We conclude that epidemic
monitoring, simulation, and forecasting are wicked problems, as applying a
conventional data-driven approach to a complex system with non-linear dynamics,
network effects, and uncertainty can be misleading. Nevertheless, some of the
errors can be corrected for, using scientific knowledge of the spreading
dynamics and the measurement process. We conclude that such corrections should
generally be part of epidemic monitoring, modeling, and forecasting efforts.
