EasyModelAnalysis does exactly what it says: it makes model analysis easy. Want to know the first time the number of infected individuals is about 1000? What is the probability that more than 50 people will be infected given probability distributions for the parameters? What variables are the most sensitive? Please find the parameters that best fit the model to the data. All of these, and more, given as simple one-liner queries over SciML-defined differential equation models.
For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation which contains the unreleased features.
using EasyModelAnalysis
@parameters t σ ρ β
@variables x(t) y(t) z(t)
D = Differential(t)
eqs = [D(D(x)) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z]
@named sys = ODESystem(eqs)
sys = structural_simplify(sys)
u0 = [D(x) => 2.0,
x => 1.0,
y => 0.0,
z => 0.0]
p = [σ => 28.0,
ρ => 10.0,
β => 8 / 3]
tspan = (0.0, 100.0)
prob = ODEProblem(sys, u0, tspan, p, jac = true)
phaseplot_extrema(prob, x, (x, y))
plot_extrema(prob, x)
