# 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 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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