The influence of assumptions on generation time distributions in epidemic models

•A simple class of stochastic models for epidemic spread is formulated.•Assumptions about times between primary and secondary infections are studied.•The influence of basic assumptions on the epidemic curve is illustrated.•Estimates of the generation time density and related parameters are derived.

A simple class of stochastic models for epidemic spread in finite, but large, populations is studied. The purpose is to investigate how assumptions about the times between primary and secondary infections influences the outcome of the epidemic. Of particular interest is how assumptions of individual variability in infectiousness relates to variability of the epidemic curve. The main concern is the final size of the epidemic and the time scale at which it evolves. The theoretical results are illustrated by simulations.