probnum.problems.zoo.diffeq.seir(t0=0.0, tmax=200.0, y0=None, 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 \(f\).

  • t0 – Initial time.

  • tmax – Final time.

  • y0(shape=(4, )) – Initial value. Defaults to [998, 1, 1, 0].

  • params – Parameters \((\alpha, \beta, \gamma)\) of the SEIR model.


InitialValueProblem object describing the SEIR model with the prescribed configuration.

Return type