# The French Covid-19 data

## The hospital data

This tool allows an interactive visualization of hospital data provided by Santé Publique France.

Data used are:

- the daily number of newly hospitalized patients,
- the daily number of patients newly admitted to intensive care units,
- the daily number of deceased patients,
- the daily number of discharded patients.

### The model

\[ \begin{align} \ddot{I}_{\rm hosp}(t) & = k_{\rm hosp}(t) \, \dot{I}_{\rm hosp}(t) \\ \ddot{I}_{\rm icu}(t) & = k_{\rm icu}(t) \, \dot{I}_{\rm icu}(t) \\ \dot{H}(t) & = \dot{I}_{\rm hosp}(t) + \dot{I}_{\rm icu}(t) - k_{\rm death}(t)H(t) - k_{\rm out}H(t) \\ \dot{D}(t) & = k_{\rm death}(t)H(t) \\ \dot{O}(t) & = k_{\rm out}(t)H(t) \\ \end{align} \] where

- \(I_{\rm hosp}(t)\) is the total (i.e. cumulated) number of individuals hospitalized at time \(t\), i.e. between time 0 and time \(t\),
- \(I_{\rm icu}(t)\) is the total number of individuals admitted to intensive care units between time 0 and time \(t\),
- \(H(t)\) is the number of individuals in hospital or in intensive care unit at time \(t\),
- \(D(t)\) is the total number of deceased individuals at time \(t\).
- \(O(t)\) is the total number of individuals who have returned home (discharges) at time \(t\).

The rate functions \(k_{\rm hosp}\) and \(k_{\rm icu}\), the death rate \(k_{\rm death}\) and the discharge rate \(k_{\rm out}\) are continuous piecewise linear functions:

\[ \begin{align} k_{\rm hosp}(t) &= a_{\rm hosp} + b_{\rm hosp} t + \sum_{k=1}^{K-1} h_{{\rm hosp}, k} ( t - \tau_{{\rm hosp}, k}) \times {\Large 1} \{t\geq \tau_{{\rm hosp}, k} \} \\ k_{\rm icu}(t) &= a_{\rm icu} + b_{\rm icu} t + \sum_{k=1}^{K-1} h_{{\rm icu}, k} ( t - \tau_{{\rm icu}, k}) \times {\Large 1} \{t\geq \tau_{{\rm icu}, k} \} \\ k_{\rm death}(t) &= a_{\rm death} + b_{\rm death} t + \sum_{k=1}^{K-1} h_{{\rm death}, k} ( t - \tau_{{\rm death}, k}) \times {\Large 1} \{t\geq \tau_{{\rm death}, k} \} \\ k_{\rm out}(t) &= a_{\rm out} + b_{\rm out} t + \sum_{k=1}^{K-1} h_{{\rm out}, k} ( t - \tau_{{\rm out}, k}) \times {\Large 1} \{t\geq \tau_{{\rm out}, k} \} \end{align} \\ \]

According to the model, \(\dot{I}_{\rm hosp}(t_j)\), \(\dot{I}_{\rm icu}(t_j)\), \(\dot{D}(t_j)\) and \(\dot{O}(t_j)\) are the predicted numbers of, respectively, newly hospitalized, newly admitted to intensive care units, deceased patients and discharged patient, between time \(t_{j-1}\) and time \(t_j\), i.e. on day \(j\).

## The EHPAD data

The data are the daily numbers of deaths in the French EHPADs (residential care facilities for dependent elderly people).
They are provided by the *Ministère des Solidarités et de la Santé* and can be downloaded here

# The global Covid-19 data

Coronavirus COVID-19 Global Cases by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU)

This Shiny application has been developed by Marc Lavielle,

Inria Saclay & Ecole Polytechnique, Xpop team

December 21st, 2020

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