Modelling the extremes of seasonal viruses and hospital congestion: The example of flu in a Swiss hospital

Abstract

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 3 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 flu cases. 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