Correlation equations for endemic diseases: externally imposed and internally generated heterogeneity

The simple susceptible-infectious-recovered (SIR) model has provided many i nsights into the behaviour of a single epidemic. However, most of epidemiol ogy is concerned with endemic infections, and for this to occur fresh susce ptibles need to be generated. This is usually provided by individuals becom ing susceptible soon after birth or by recruitment to cohorts at risk. This paper develops a correlation model, predicting the behaviour of connected pairs of individuals, which includes demographic processes as well as the b asic epidemiology. In addition to the local spatial correlations, we consid er three other forms of heterogeneity: internally generated heterogeneity i n terms of stochasticity or imposed heterogeneity in terms of non-uniform v accination or age-structure.