Predictability: Can the turning point and end of an expanding epidemic be precisely forecast?

Castro, Mario; Ares, Sa'ul; Cuesta, Jos'e A.; Manrubia, Susanna

No, they can't. Exponentially growing dynamics are intrinsically unpredictable. The time at which the number of infected individuals starts decreasing cannot be reliably calculated before it is actually attained. A standard SIR model with confinement shows that infection spread is inhibited only above a threshold. Confinement induces a slow-down in the expansion phase that does not guarantee an eventual control of the epidemic. A Bayesian fit to the on-going COVID-19 pandemic in Spain shows that we can infer neither its peaking time nor whether there is a peak at all. The dispersion of possible trajectories grows extremely fast, yielding a short horizon for reliable prediction. As unpredictability is intrinsic, not due to incomplete or wrong data, our study advocates for a scenario of probabilistic forecasting.