Functions of variables in @mtkmodel

Specific Domains Modelling & Simulations
1

I’m playing with the new (at least to me) @mtkmodel syntax. Here’s my standard SIR model.

using Symbolics
using ModelingToolkit: t_nounits  as t, D_nounits as D
using OrdinaryDiffEq
using Plots

@mtkmodel SIR begin
    @parameters begin
        β
        γ
    end
    @variables begin
        S(t)
        I(t)
        R(t)
    end
    @equations begin
        D(S) ~ -β * S * I
        D(I) ~ β * S * I - γ * I
        D(R) ~ γ * I
    end
end

@mtkbuild sir=SIR()
prob = ODEProblem(sir,
                 [sir.S => 990.0, sir.I => 10.0, sir.R => 0.0],
                 (0.0, 40.0),
                 [sir.β => 0.0005, sir.γ => 0.25])
sol = solve(prob, Tsit5())
plot(sol)

I want to define the model like this:

@equations begin
        D(S) ~ -β * S * I/N
        D(I) ~ β * S * I/N - γ * I
        D(R) ~ γ * I
    end

where N=S+I+R. In the non-DSL version, I just write this:

@variables S(t), I(t), R(t)
N = S + I + R

How do I introduce N into @mtkmodel?

2

Make that an observed equation in the equations set