Recurrent outbreaks of childhood diseases revisited: The impact of isolation

The recurrent outbreaks of measles and other childhood diseases have previously been explained by an interaction of intrinsic epidemiologic forces generating dampened oscillations and of seasonal and/or stochastic excitation. We show that isolation (i.e., sick individuals stay at home and have a reduced infective impact) can create self-sustained oscillations provided that the number of per capita contacts is largely independent of the number of individuals present. This means that the bilinear mass action term for disease incidence is modified by dividing it by the number of nonisolated individuals.