Simulation

From transitions to ODEs

Given compartments [C1, C2, ..., Ck] and transitions A->B: expr, we compute for each compartment the net rate:

• For A subtract expr
• For B add expr

The result is a system:

\[ \frac{d\mathbf{y}}{dt} = f(t, \mathbf{y}; \theta) \]

where \(\mathbf{y} = [S, I, R, ...]\) and \(\theta\) are the parameters.

Solver

The default solver is scipy.integrate.odeint (LSODA). Usage example:

from scipy.integrate import odeint
import numpy as np

def rhs(y, t, params):
    S, I, R = y
    beta, gamma = params['beta'], params['gamma']
    N = params['N']
    dSdt = -beta * S * I / N
    dIdt = beta * S * I / N - gamma * I
    dRdt = gamma * I
    return [dSdt, dIdt, dRdt]

t = np.linspace(0, days, days+1)
y0 = [990, 10, 0]
sol = odeint(rhs, y0, t, args=( {'beta':0.3,'gamma':0.1,'N':1000}, ))

Time-dependent parameters

If your model requires time-varying parameters, provide an extras_fn(t, y) hook that returns a dict of parameter values at t. The rhs should consult those values when computing rates.