Coupling of Two Sir Epidemic Models with Variable Susceptibilities and Infectivities

The variable generalised stochastic epidemicmodel, which allows for variability in both the susceptibilities and infectivities of individuals, is analysed. A very different epidemic modelwhich exhibits variable susceptibility and infectivity is the random-graph epidemic model. A suitable coupling of the two epidemic models is derived which enables us to show that, whilst the epidemics are very different in appearance, they have the same asymptotic final size distribution. The coupling provides a novel approach to studying random-graph epidemic models.