Initial conditions as functions of parameters in ModelingToolkit?

Specific Domains Modelling & Simulations
1

Hi everyone,

Is it possible to have initial conditions as functions of the parameters in ModelingToolkit?

2

IIRC, yes. That was discussed and added? It would be good to have it in an example or tutorial though.

3

Hmm, it appears to ‘just work’ now that I tried the obvious thing :slight_smile:

using ModelingToolkit
using OrdinaryDiffEq
using Plots

@parameters t R₀ γ μ a
@variables S(t) I(t) β(t)
D = Differential(t)

eqs = [D(S) ~ μ - β*S*I - μ*S,
       D(I) ~ β*S*I - (γ+μ)*I,
       β ~ R₀*(γ+μ)*(1+a*cos(2*π*t))]

@named sys = ODESystem(eqs)
simpsys = structural_simplify(sys)

S₀ = 1/R₀
I₀ = (μ/(μ+γ))*(1-S₀)
u₀ = [S => S₀, I => I₀]
p = [μ => 0.02, γ => 28.08, R₀ => 17.0, a => 0.08]
tspan = (0.0, 100.0)

prob = ODEProblem(simpsys, u₀, tspan, p)
sol = solve(prob, Rosenbrock23())

plot(sol, yscale=:log10)

sirforced

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