Confidence in the dynamic spread of epidemics under biased sampling conditions

Brunner, James D.; Chia, Nicholas

The interpretation of sampling data plays a crucial role in policy response to the spread of a disease during an epidemic, such as the COVID-19 epidemic of 2020. However, this is a non-trivial endeavor due to the complexity of real world conditions and limits to the availability of diagnostic tests, which necessitate a bias in testing favoring symptomatic individuals. A thorough understanding of sampling confidence and bias is necessary in order make accurate conclusions. In this manuscript, we provide a stochastic model of sampling for assessing confidence in disease metrics such as trend detection, peak detection, and disease spread estimation. Our model simulates testing for a disease in an epidemic with known dynamics, allowing us to use Monte-Carlo sampling to assess metric confidence. We use this method to show that trends in the disease may be identified using under $10000$ biased samples each day, and an estimate of disease spread can be made with additional $1000-2000$ unbiased samples each day. We also demonstrate that the model can be used to assess more advanced metrics by finding the precision and recall of a strategy for finding peaks in the dynamics.