Chaotic dynamics in the seasonally forced SIR epidemic model.

We prove analytically the existence of chaotic dynamics in the forced SIR model. Although numerical experiments have already suggested that this model can exhibit chaotic dynamics, a rigorous proof (without computer-aided) was not given before. Under seasonality in the transmission rate, the coexistence of low birth and mortality rates with high recovery and transmission rates produces infinitely many periodic and aperiodic patterns together with sensitive dependence on the initial conditions.