The Relevance of Stochastic Models for Large-Scale Epidemiological Phenomena

The extent is discussed to which stochastic, as distinct from deterministic, epidemic models are needed in the explanation of large‐scale epidemiological phenomena. The possible extinction of infection seems the most relevant factor, as not only does this properly account for the bifurcation in behaviour above the threshold (the principle of which is extended to the host and intermediate vector case), but it gives rise also to the concept of critical community size in the theory of recurrent epidemics such as measles. While deterministic models are adequate for some purposes when extinction is absent, the theoretical study of long‐term epidemic patterns may still be impossible without the more complete stochastic versions; this is illustrated by reference to a provisional model for chickenpox.