Delayed epidemic peak caused by infection and recovery rate fluctuations

Forecasting epidemic scenarios has been critical to many decision-makers in imposing various public health interventions. Despite progresses in determining the magnitude and timing of epidemics, epidemic peak time predictions for H1N1 and COVID-19 were inaccurate, with the peaks delayed with respect to predictions. Here, we show that infection and recovery rate fluctuations play a critical role in peak timing. Using a susceptible-infected-recovered model with daily fluctuations on control parameters, we show that infection counts follow a lognormal distribution at the beginning of an epidemic wave, similar to price distributions for financial assets. The epidemic peak time of the stochastic solution exhibits an inverse Gaussian probability distribution, fitting the spread of the epidemic peak times observed across Italian regions. We also show that, for a given basic reproduction number R₀, the deterministic model anticipates the peak with respect to the most probable and average peak time of the stochastic model. The epidemic peak time distribution allows one for a robust estimation of the epidemic evolution. Considering these results, we believe that the parameters' dynamical fluctuations are paramount to accurately predict the epidemic peak time and should be introduced in epidemiological models.