  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, and a Generalized Pareto distribution for the odds
of positive 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 introduced
approach could be applied to several types of seasonal disease data such as
those derived from the new virus SARS-CoV-2 and its COVID-19 disease which is
at the moment wreaking havoc worldwide. The empirical effectiveness of the
proposed method is assessed through a simulation study.
