The final size of an epidemic in a heterogeneous society

This note describes the outcome of an epidemic in a heterogeneous population with a very simple structure. The population is split into two sections in which the epidemic runs a different course. The reproduction numbers of the two epidemics are unobserved, only the overall reproduction number is known. For such a population the outcome of the epidemic can be as well far worse as far better than expected on the basis of the overall reproduction number. By considering a very simple model of this population some calculations are feasible under general assumptions on the epidemic itself. These calculations show in which direction models based on the overall reproduction number can misrepresent the real-world situation.