Classical mean-field epidemic theory upper-bounds real disease spread

Non-Markovian theory provides the most accurate stochastic description of an infection spreading on a contact graph with a general distribution of the infection time and curing time. However, the infection time is not directly measurable and instead the generation time is measured in real-world epidemics. Here we show that if the generation time follows approximately a Weibull distribution with shape parameter α, then the Weibull infection time of the spreading process possesses a similar shape parameter α. For a large list of published generation times in biological, mainly respiratory epidemics, the Weibull shape parameter α is computed, which reveals that nearly always α > 1. The impact of this observation is that a complicated non-Markovian analysis is not needed, because the well-established Markovian case α = 1 provides a lower bound for the epidemic threshold and an upper bound for the basic reproduction number and the nodal infection probabilities in the contact graph. Non-Markovian theory models epidemic spread on contact graphs with varied infection and curing times. Generation times measured from many real diseases are shown to follow a Weibull distribution with shape parameter α>1, implying that the simpler Markovian theory (α=1) suffices to provide reliable bounds for epidemic predictions.