Positive test cases are the foundation for calculating the total number of infections, as well as for trending the number of infections. However, test cases account for only a fraction of total infections, due to many people being asymptomatic and not seeking testing, limited test availability early in the pandemic, state strategies of testing only high risk individuals, and other factors.
Positive Test Percentage (“Positivity”). The percentage of virus tests that show positive results (“positivity”) is an indicator of what percentage of the total infections is being identified through testing. The higher the positivity is, the lower the percentage of overall infections being detected is. Most states started with high positivity and now have positivities in the range of 2.5-10% . This implies the overall infections are 7-10 times higher than the number of positive tests.
To estimate the total number of infections, I use two models.
Infection Model 1 estimates infections based on the number of deaths 13 days after the date of the infection report (the day most test results are reported that later result in those deaths). Infections are calculated as the number of people who would have needed to be infected as of that particular test date to produce the number of actual deaths 13 days later.
Infection Model 2 estimates infections based on the percentage of test results that are positive in each state. This calculation is based on a curve-fitted model derived both from multi-month state-level data and from daily test and death data, using the 13 day lag between tests and deaths.
In most instances I use the simple average of the two models as the “probable” level of infections.