Modelling the duration of time between peak hospital admissions and peak bed occupancy for seasonal epidemics: application to influenza

Purpose Hospital bed occupancy is known to trail admissions for seasonal epidemics, yet the duration of time between the respective peaks has not before been specifically investigated. As well as addressing a deficit in the literature, this information is practically useful in guiding management decisions when hospital pressures are greatest. This study aims to formulate a mathematical equation for the duration of time between peak admissions and peak bed occupancy for seasonal epidemics and to estimate this for influenza as an example. Design/methodology/approach The temporal profile of bed occupancy was modelled as a convolution of the epidemic’s admissions profile and length of stay distribution. This was calibrated to data for 4,858 influenza admissions sourced from a one-million-resident health-care system in England for the 2015/2016–2023/2024 seasons. Findings Modelling reveals a one-week duration (7.09-day median and 6.98-day mean) between peak admissions and peak bed occupancy for seasonal influenza epidemics. Variation is mainly driven by the shape of the admissions profile, with shorter (longer) durations associating with steeper (flatter) admissions peaks. The normal distribution is relatively unsuitable for approximating the admissions profile, with better results for the Cauchy distribution. The Weibull distribution is most appropriate for representing lengths of stay. Originality/value A parsimonious mathematical model was developed with demonstrated application for influenza. This provides hospital management with novel insights to support operational preparedness for seasonal epidemics.