Step 1: The description - contacts falling ill within one incubation period after an index case - points to a measure of how readily the disease spreads to close contacts.
Step 2: That measure is the secondary attack rate, which counts susceptible contacts who develop disease within the incubation window after exposure to the primary case, divided by all susceptibles exposed.
Step 3: It is widely used to gauge the communicability of an infection, particularly in household and institutional outbreaks.
Step 4: The case fatality rate deals with deaths and the primary attack rate concerns the first wave of cases, so neither fits; the answer is the secondary attack rate.
\[\boxed{\text{Secondary attack rate}}\]