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

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Abstract
The simple susceptible–infectious–recovered (SIR) model has provided many insights into the behaviour of a single epidemic. However, most of epidemiology is concerned with endemic infections, and for this to occur fresh susceptibles need to be generated. This is usually provided by individuals becoming 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 basic epidemiology. In addition to the local spatial correlations, we consider three other forms of heterogeneity: internally generated heterogeneity in terms of stochasticity or imposed heterogeneity in terms of non-uniform vaccination or age–structure.

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