The RTOfSickCasesOpen measure gives me exactly what I need, a running total number of sick cases open per reporting date, regardless of when the first sick day occurred. Both other measure are just intermediate measures I'm not going to need when creating the dashboard.
A cleaner option would be to create just one measure RTOfSickCasesOpen, with the other intermediate measures as variables.
VAR NumOfSickCasesReported =
VAR NumOfSickCasesOpen =
ALL ( SickCases[RecoveryDate] ),
SickCases[RecoveryDate] > MAX ( Calendar12M[Date] )
VAR RTOfSickCasesOpen =
ALL( Calendar12M[Date] ),
Calendar12M[Date] <= MAX ( Calendar12M[Date] )
However, this cleaner version of RTOfSickCasesOpen doesn't seem to work as expected.