Modelling the Extremes of Seasonal Viruses and Hospital Congestion: The Example of Flu in a Swiss Hospital

Viruses causing flu or milder coronavirus colds are often referred to as “seasonal

viruses” as they tend to subside in warmer months. In other words, meteorological

conditions tend to impact the activity of viruses, and this information can be exploited

for the operational management of hospitals. In this study, we use three years

of daily data from one of the biggest hospitals in Switzerland and focus on modelling

the extremes of hospital visits from patients showing flu-like symptoms and the

number of positive cases of flu. We propose employing a discrete Generalized Pareto

distribution for the number of positive and negative cases. Our modelling framework

allows for the parameters of these distributions to be linked to covariate effects, and

for outlying observations to be dealt with via a robust estimation approach. Because

meteorological conditions may vary over time, we use meteorological and not

calendar variations to explain hospital charge extremes, and our empirical findings

highlight their significance. We propose a measure of hospital congestion and a

related tool to estimate the resulting CaRe (Charge-at-Risk-estimation) under different

meteorological conditions. The relevant numerical computations can be easily

carried out using the freely available GJRM R package. The empirical effectiveness of

the proposed method is assessed through a simulation study.