The rate of convergence to early asymptotic behaviour in age-structured epidemic models

Age structure is incorporated in many types of epidemic model. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of dynamical systems theory to show that for some reasonable parameter values, this convergence can be slow. Such a possibility should therefore be considered when parameterising age-structured epidemic models.