SEIR disease model

  

      This project presents an interactive SEIR model trying to match Cornavirus data from Italy.
      

      Data from Italy are plotted in black.  
      

      Please note that I am not epidemiologist, the parameters might be wrong and the actions 
      for containements are not taken into account  ..
      If some epidemilogists could validate and contribute to this work .. it would be great !
      We need to know where we are going !
      

      Link to source code available below

The plot below shows the number of Italy (data), Susceptible (model), Exposed (model), Infectious (model), and Resistant (model) individuals over time (in days) as percentages of the entire population.

Parameters

R₀: Latent period $\left(\frac{1}{\alpha}\right)$: Infectious period $\left(\frac{1}{\gamma}\right)$: Duration of resistance $\left(\frac{1}{\sigma}\right)$: Mixing exponent $\left(\eta\right)$: Initial susceptibility $\left(S(t=0)\right)$: Days: Upper bound for Y axis: %

Equations

$\begin{align*} \beta &= R_0 \cdot \gamma \\ \frac{{d\class{varS}{S}}}{dt} &= - \beta \class{varI}{I} \cdot \left(\frac{\class{varS}{S}}{N}\right)^\eta + \sigma \class{varR}{R} \\ \frac{d\class{varE}{E}}{dt} &= \beta \class{varI}{I} \cdot \left(\frac{\class{varS}{S}}{N}\right)^\eta - \alpha \class{varE}{E} \\ \frac{d\class{varI}{I}}{dt} &= \alpha \class{varE}{E} - \gamma \class{varI}{I} \\ \frac{d\class{varR}{R}}{dt} &= \gamma \class{varI}{I} - \sigma \class{varR}{R} \\ \end{align*}$