I went to sleep last night reading an undergraduate textbook on differential equations. Throughout the book, the author did a very good job showing how differential equations can be very useful in creating mathematical models for real world phenomena. When I woke up this morning one of the first things I saw was an online newspaper headline stating “Positive [COVID-19] tests hit new high in state.” This got me thinking. Things usually go downhill when this happens (me thinking that is). Smart people, like those here on the SDMB, understand that there are at least two reasons for increasing numbers of positive tests: (1) more people have contracted the disease, and (2) more people are being tested for the disease. (I suspect that some newspaper headline authors, some non-SDMB people, and politicians never thought about this.) How do professional epidemiologists account for the increasing number tests being conducted when constructing a mathematical model that predicts the spread of a contagious disease? Especially when testing resources are limited, people who are at risk for more debilitating effects from the disease, rich people, people who are in greater contact with the general population, politicians, people with critical skills, etc. might be preferentially tested.
This question is not necessarily about the COVID-19 virus, however moderators are welcome to move this post as they see fit.