# Functions of variables in @mtkmodel
**URL:** https://discourse.julialang.org/t/functions-of-variables-in-mtkmodel/117159
**Category:** Modelling & Simulations
**Created:** [July 17, 2024, 8:04pm UTC](https://discourse.julialang.org/t/functions-of-variables-in-mtkmodel/117159 "2024-07-17T20:04:15Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@sdwfrost](https://discourse.julialang.org/u/sdwfrost)
#### Post date: [July 17, 2024, 8:04pm UTC](https://discourse.julialang.org/t/functions-of-variables-in-mtkmodel/117159/1 "2024-07-17T20:04:15Z")
I’m playing with the new (at least to me) `@mtkmodel` syntax. Here’s my standard SIR model.
```Julia
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:
```Julia
@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:
```Julia
@variables S(t), I(t), R(t)
N = S + I + R
```
How do I introduce N into `@mtkmodel`?
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 17, 2024, 8:31pm UTC](https://discourse.julialang.org/t/functions-of-variables-in-mtkmodel/117159/2 "2024-07-17T20:31:17Z")
Make that an observed equation in the equations set