Determinants of periodicity in seasonally driven epidemics

► We study the forced SIR model near the transition from annual to biennial dynamics. ► A simple prediction of the threshold between annual and biennial is analytically derived. ► Prediction is given in terms of key epidemiological parameters. ► Thus a sufficient decrease in either birth-rate or R0 will induce the transition. ► Predicted effects are in accord with empirical observations and simulations.