With the spread of COVID-19 across the world, a large amount of data on reported cases has become available. We are studying here a potential bias induced by the daily number of tests which may be insufficient or vary over time. Indeed, tests are hard to produce at the early stage of the epidemic and can therefore be a limiting factor in the detection of cases. Such a limitation may have a strong impact on the reported cases data. Indeed, some cases may be missing from the official count because the number of tests was not sufficient on a given day. In this work, we propose a new differential equation epidemic model which uses the daily number of tests as an input. We obtain a good agreement between the model simulations and the reported cases data coming from the state of New York. We also explore the relationship between the dynamic of the number of tests and the dynamics of the cases. We obtain a good match between the data and the outcome of the model. Finally, by multiplying the number of tests by 2, 5, 10, and 100 we explore the consequences for the number of reported cases.
Clarifying predictions for COVID-19 from testing data: The example of New York State