  In this work, we study the unpredictability of seasonal infectious diseases
considering a SEIRS model with seasonal forcing. To investigate the dynamical
behaviour, we compute bifurcation diagrams type hysteresis and their respective
Lyapunov exponents. Our results from bifurcations and the largest Lyapunov
exponent show bistable dynamics for all the parameters of the model. Choosing
the inverse of latent period as control parameter, over 70% of the interval
comprises the coexistence of periodic and chaotic attractors, bistable
dynamics. Despite the competition between these attractors, the chaotic ones
are preferred. The bistability occurs in two wide regions. One of these regions
is limited by periodic attractors, while periodic and chaotic attractors bound
the other. As the boundary of the second bistable region is composed of
periodic and chaotic attractors, it is possible to interpret these critical
points as tipping points. In other words, depending on the latent period, a
periodic attractor (predictability) can evolve to a chaotic attractor
(unpredictability). Therefore, we show that unpredictability is associated with
bistable dynamics preferably chaotic, and, furthermore, there is a tipping
point associated with unpredictable dynamics.
