# seir¶

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 $$f$$.

Parameters
• 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 $$(\alpha, \beta, \gamma)=(0.3, 0.3, 0.1)$$.

Returns

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

Return type

IVP