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We study the unpredictability of seasonal infectious diseases using a SEIRS model with seasonal forcing. We compute bifurcation diagrams and Lyapunov exponents. We show bistable dynamics for all the model parameters. The bistability occurs in two wide regions. One of these regions is limited by periodic attractors, while periodic and chaotic attractors bound the other. The analyzed range displays that the latent period is a crucial variable to understand the unpredictability of infectious diseases. We identify a tipping point associated with unpredictable dynamics.