Dynamics of COVID‐19 epidemics: SEIR models underestimate peak infection rates and overestimate epidemic duration

Compartment models of infectious diseases, such as SEIR, are being used extensively to model the COVID‐19 epidemic. Transitions between compartments are modelled either as instantaneous rates in differential equations, or as transition probabilities in discrete time difference or matrix equations. These models give accurate estimates of the position of equilibrium points, when the rate at which individuals enter each stage is equal to the rate at which they exit from it. However, they do not accurately capture the distribution of times that an individual spends in each compartment, so do not accurately capture the transient dynamics of epidemics. Here we show how matrix models can provide a straightforward route to accurately model stage durations, and thus correctly reproduce epidemic dynamics. We apply this approach to modelling the dynamics of a COVID‐19 epidemic. We show that a SEIR model overestimates epidemic durations and substantially underestimates peak infection rates, by factors of 2 and 3 respectively using published parameter estimates based on the progress of the epidemic in Wuhan.