Epidemic models often reflect characteristic features of infectious spreading processes by coupled nonlinear differential equations considering different states of health (such as susceptible, infectious or recovered). This compartmental modelling approach, however, delivers an incomplete picture of the dynamics of epidemics, as it neglects stochastic and network effects, and 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 combine established epidemiological spreading models with a measurement model of the 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 fundamental limitations of purely data-driven methods when assessing 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 nonlinear 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, modelling and forecasting efforts. This article is part of the theme issue 'Data science approaches to infectious disease surveillance'.
Keywords: complex systems; computer simulation; data science; epidemic modelling; network theory; statistics.