Some model based considerations on observing generation times for communicable diseases.

The generation time of an infectious disease is usually defined as the time from the moment one person becomes infected until that person infects another person. The concept is similar to "generation gap" in demography, with new infections replacing births in a population. Originally applied to diseases such as measles where at least the first generations are clearly discernible, the concept has recently been extended to other diseases, such as influenza, where time order of infections is usually much less apparent. By formulating the relevant statistical questions within a simple yet basic mathematical model for infection spread, it is possible to derive theoretical properties of observations in various situations e.g. in "isolation", in households, or during large outbreaks. In each case, it is shown that the sampling distribution of observations depends on a number of factors, usually not considered in the literature and that must be taken into account in order to achieve unbiased inference about the generation time distribution. Some implications of these findings for statistical inference methods in epidemic spread models are discussed.