# seir¶

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 $$f$$.

Parameters
• 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.

Returns

InitialValueProblem object describing the SEIR model with the prescribed configuration.

Return type

InitialValueProblem