Symbolic

In [1]:

import sympy

from mxlpy import Model, fns, symbolic, to_symbolic_model


def sir() -> Model:
    return (
        Model()
        .add_variables({"s": 0.9, "i": 0.1, "r": 0.0})
        .add_parameters({"beta": 0.2, "gamma": 0.1})
        .add_reaction(
            "infection",
            fns.mass_action_2s,
            args=["s", "i", "beta"],
            stoichiometry={"s": -1, "i": 1},
        )
        .add_reaction(
            "recovery",
            fns.mass_action_1s,
            args=["i", "gamma"],
            stoichiometry={"i": -1, "r": 1},
        )
    )


symbolic_model = to_symbolic_model(sir())
symbolic_model.jacobian()

import sympy from mxlpy import Model, fns, symbolic, to_symbolic_model def sir() -> Model: return ( Model() .add_variables({"s": 0.9, "i": 0.1, "r": 0.0}) .add_parameters({"beta": 0.2, "gamma": 0.1}) .add_reaction( "infection", fns.mass_action_2s, args=["s", "i", "beta"], stoichiometry={"s": -1, "i": 1}, ) .add_reaction( "recovery", fns.mass_action_1s, args=["i", "gamma"], stoichiometry={"i": -1, "r": 1}, ) ) symbolic_model = to_symbolic_model(sir()) symbolic_model.jacobian()

Out[1]:

$\displaystyle \left[\begin{matrix}- 1.0 \beta i & - 1.0 \beta s & 0\\1.0 \beta i & 1.0 \beta s - 1.0 \gamma & 0\\0 & 1.0 \gamma & 0\end{matrix}\right]$

Identifiability¶

In [2]:

res = symbolic.check_identifiability(
    symbolic_model,
    outputs=[sympy.Symbol("i"), sympy.Symbol("r")],
)
print(res.summary())

res = symbolic.check_identifiability( symbolic_model, outputs=[sympy.Symbol("i"), sympy.Symbol("r")], ) print(res.summary())

Main loop: 0it [00:00, ?it/s]

Main loop: 2it [00:00, 32.10it/s]

Summary
=======
The model is not FISPO.
Identifiable parameters: [beta, gamma]
Unidentifiable parameters: []
Identifiable variables: [s, i, r]
Unidentifiable variables: []
Identifiable inputs: []
Unidentifiable inputs: []