autosim.simulations.seir

SEIR epidemic simulator and ODE helper functions.

simulate_seir_epidemic(x, N=1000, I0=1, E0=0)

Simulate an epidemic using the SEIR model.

The compartment dynamics are:

\[\begin{split}\begin{aligned} \frac{dS}{dt} &= -\beta S I / N \\ \frac{dE}{dt} &= \beta S I / N - \sigma E \\ \frac{dI}{dt} &= \sigma E - \gamma I \\ \frac{dR}{dt} &= \gamma I \end{aligned}\end{split}\]

Parameters:

• x (ndarray) – SEIR parameters [beta, gamma, sigma].

• N (int) – Total population.

• I0 (int) – Initial infected.

• E0 (int) – Initial exposed.

Returns:

Peak infection fraction I_max / N.

Return type:

float

class SEIRSimulator(parameters_range=None, output_names=None, log_level='progress_bar')

Bases: Simulator

Simulator of infectious disease spread using the SEIR model.

The compartment dynamics are:

\[\begin{split}\begin{aligned} \frac{dS}{dt} &= -\beta S I / N \\ \frac{dE}{dt} &= \beta S I / N - \sigma E \\ \frac{dI}{dt} &= \sigma E - \gamma I \\ \frac{dR}{dt} &= \gamma I \end{aligned}\end{split}\]

The simulator returns the peak infection rate as a fraction of the total population.

Parameters:

log_level (str)