Population induced oscillations in blended SI-SEI epidemiological models

The effects of standard patterns of population growth in blended SI–SEI models (of which models for ‘fast and slow’ tuberculosis are an instance) are considered. When the incidence has the ‘true mass action’ form, the system is globally stable under both exponential and logistic population dynamics, whereas sustained oscillations occur in the case of bilinear incidence. This shows in the final analysis, the minimal dynamical ingredients needed to generate oscillations in basic epidemiological models: provided the population is exponentially growing and the incidence is bilinear, at least a fraction of the newly exposed individuals must enter the infective state with a delay.