probnum.diffeq.seir(timespan, initrv, params=0.3, 0.3, 0.1)[source]

Initial value problem (IVP) based on the SEIR model.

The SEIR model with no vital dynamics is defined through

\[\begin{split}f(t, y) = \begin{pmatrix} \frac{-\beta y_1 y_3}{N} \\ \frac{\beta y_1 y_3}{N} - \alpha y_2 \\ \alpha y_2 - \gamma y_3 \\ \gamma y_3 \end{pmatrix}\end{split}\]

for some parameters \((\alpha, \beta, \gamma)\) and population count \(N\). Without taking vital dynamics into consideration, \(N\) is constant such that for every time point \(t\)

\[S(t) + E(t) + I(t) + R(t) = N\]

holds. Default parameters are \((\alpha, \beta, \gamma)=(0.3, 0.3, 0.1)\). The population count is computed from the (mean of the) initial value random variable. This implementation includes the Jacobian \(J_f\) of \(f\).

  • timespan ((float, float)) – Time span of IVP.

  • initrv (RandomVariable,) – (shape=(4, )) – Vector-valued RandomVariable that describes the belief over the initial value. Usually it is a Constant (noise-free) or Normal (noisy) Random Variable with \(4\)-dimensional mean vector and \(4 \times 4\)-dimensional covariance matrix. To replicate “classical” initial values use the Constant distribution.

  • params ((float, float, float), optional) – Parameters \((\alpha, \beta, \gamma)\) for the SEIR model IVP. Default is \((\alpha, \beta, \gamma)=(0.3, 0.3, 0.1)\).


IVP object describing the SEIR model IVP with the prescribed configuration.

Return type