# 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

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

- \(I_{\rm hosp}\) is the total (i.e. cumulated) number of infected individuals who will be hospitalized
- \(I_{\rm icu}\) is the total number of infected individuals who will be admitted to intensive care units
- \(H\) is the number of individuals in hospital or in intensive care unit
- \(D\) is the total number of deceased individuals.
- \(O\) is the total number of individuals who have returned home (discharges).

Rate functions \(k_{\rm hosp}\) and \(k_{\rm icu}\) are continuous piecewise linear functions:

\[ \begin{align} k_{\rm hosp}(t) &= k_{\rm hosp, 0} + a_{\rm hosp} t + \sum_{k=1}^{K-1} h_{{\rm hosp}, k} ( t - \tau_{{\rm hosp}, k}) \times {\Large 1} \{t\geq \tau_{{\rm hosp}, k} \} \\ k_{\rm icu}(t) &= k_{\rm icu, 0} + a_{\rm icu} t + \sum_{k=1}^{K-1} h_{{\rm icu}, k} ( t - \tau_{{\rm icu}, k}) \times {\Large 1} \{t\geq \tau_{{\rm icu}, k} \} \end{align} \]

The death rate \(k_{\rm deaths}\) and the discharge rate \(k_{\rm out}\) are (decreasing - increasing) functions of time:

\[ k_{\rm deaths}(t) = \left\{ \begin{array}{cc} \mu_1 e^{-\alpha_1 \, t } & {\rm if } \quad t \leq \gamma \\ \mu_1 e^{\alpha_2 t - (\alpha_1+\alpha_2) \gamma} & {\rm if } \quad t \geq \gamma \end{array} \right. \]

\[ k_{\rm out}(t) = \left\{ \begin{array}{cc} \nu_1 e^{-\beta_1 \, t } & {\rm if } \quad t \leq \gamma \\ \nu_1 e^{\beta_2 t - (\beta_1+\beta_2) \gamma} & {\rm if } \quad t \geq \gamma \end{array} \right. \]

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

September 19th, 2020