# How to link observables with ODE to make interactive plot?

**URL:** <https://discourse.julialang.org/t/how-to-link-observables-with-ode-to-make-interactive-plot/111043>\
**Category:** Modelling & Simulations\
**Created:** [March 2, 2024, 6:49am UTC](https://discourse.julialang.org/t/how-to-link-observables-with-ode-to-make-interactive-plot/111043 "2024-03-02T06:49:18Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Luigi\_Marongiu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/luigi_marongiu/32/7909_2.png) [@Luigi\_Marongiu](https://discourse.julialang.org/u/Luigi_Marongiu)\
**Post date:** [March 2, 2024, 6:49am UTC](https://discourse.julialang.org/t/how-to-link-observables-with-ode-to-make-interactive-plot/111043/1 "2024-03-02T06:49:18Z")

</div>

I would like to make an interactive plot of a SIV model using GLMakie. But how can I link GLMakie with DifferentialEquations? The latter requires parameters that are passed to the solver and these parameters are made of observable. I have troubles with the links.  
I tried with the following:

```julia
julia> using GLMakie, DifferentialEquations, Parsers

julia> function odeSolver!(du, u, p, t) 
           μ = p.μ # bacterial growth rate
           κ = p.κ # bacterial carrying capacity
           ω = p.ω # system wash-out rate
           δ = p.δ # phagial infection rate
           η = p.η # phagial lysis rate (inverse latency)
           β = p.β # phagial burst size
           λ = p.λ # phagial decay rate
                       # du[1] = S; du[2] = I; du[3] = V
           ρ = 1 - (u[1] + u[2])/κ # rho: logistic factor
           ϡ = (δ*u[1]*u[3]) # upsampi : infected bacteria
           du[1] = (μ*u[1]*ρ) - ϡ - (ω*u[1])
           du[2] = ϡ - (η*u[2]) - (ω*u[2])
           du[3] = (β*η*u[2]) - ϡ - (λ*u[3]) - (ω*u[3])
       end
odeSolver! (generic function with 1 method)

julia> begin
           Mu = Observable(0.16) # μ: default growth rate
           Kappa = Observable(2.2e7) # κ: default carrying capacity
           Omega = Observable(0.05) # ω: default outflow
           Eta = Observable(0.025) # η: default τ reciprocal    
           Delta = Observable(1e-9) # δ: default adsorption rate 
           Beta = Observable(50) # β: default burst size 
           Lambda = Observable(0) # λ: default decay rate
           S0 = Observable(1e5) # default starting amount of naive bacteria
           I0 = Observable(0) # default starting amount of infected bacteria
           V0 = Observable(1e5) # default starting amount of phages
           Tm = Observable(2000.0) # default time span 
       end
Observable(2000.0)

julia> begin
           # initial amounts S, I, V
           u0 = @lift(vcat($S0, $I0, $V0))
           tspan = @lift(vcat(0.0, $Tm)) 
           parms = @lift(μ=$Mu, κ=$Kappa, ω=$Omega, δ=$Delta, η=$Eta, β=$Beta, λ=$Lambda)
       end
ERROR: LoadError: MethodError: no method matching var"@lift"(::LineNumberNode, ::Module, ::Expr, ::Expr, ::Expr, ::Expr, ::Expr, ::Expr, ::Expr)

Closest candidates are:
  var"@lift"(::LineNumberNode, ::Module, ::Any)
   @ Makie ~/.julia/packages/Makie/VRavR/src/interaction/liftmacro.jl:72

Stacktrace:
  [1] eval
    @ ./boot.jl:385 [inlined]
  [2] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
    @ Base ./loading.jl:2076
  [3] invokelatest(::Any, ::Any, ::Vararg{Any}; kwargs::@Kwargs{})
    @ Base ./essentials.jl:892
  [4] invokelatest(::Any, ::Any, ::Vararg{Any})
    @ Base ./essentials.jl:889
  [5] inlineeval(m::Module, code::String, code_line::Int64, code_column::Int64, file::String; softscope::Bool)
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:263
  [6] (::VSCodeServer.var"#67#72"{…})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:181
  [7] withpath(f::VSCodeServer.var"#67#72"{…}, path::String)
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/repl.jl:274
  [8] (::VSCodeServer.var"#66#71"{…})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:179
  [9] hideprompt(f::VSCodeServer.var"#66#71"{…})
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/repl.jl:38
 [10] (::VSCodeServer.var"#65#70"{…})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:150
 [11] with_logstate(f::Function, logstate::Any)
    @ Base.CoreLogging ./logging.jl:515
 [12] with_logger
    @ ./logging.jl:627 [inlined]
 [13] (::VSCodeServer.var"#64#69"{VSCodeServer.ReplRunCodeRequestParams})()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:255
 [14] #invokelatest#2
    @ ./essentials.jl:892 [inlined]
 [15] invokelatest(::Any)
    @ Base ./essentials.jl:889
 [16] (::VSCodeServer.var"#62#63")()
    @ VSCodeServer ~/.vscode/extensions/julialang.language-julia-1.73.2/scripts/packages/VSCodeServer/src/eval.jl:34
in expression starting at /home/gigiux/Documents/Model/MkBact_1.jl:42
Some type information was truncated. Use `show(err)` to see complete types.

```

How do I pass observable to the ODE solver?  
Thank you

---

<div class="post-metadata">

**Author:** ![xiaoming](https://avatars.discourse-cdn.com/v4/letter/x/a6a055/32.png) [@xiaoming](https://discourse.julialang.org/u/xiaoming)\
**Post date:** [March 2, 2024, 8:01am UTC](https://discourse.julialang.org/t/how-to-link-observables-with-ode-to-make-interactive-plot/111043/2 "2024-03-02T08:01:57Z")

</div>

Maybe you can try DynamicalSystems.jl. The document: [Animations, GUIs, Visuals · DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/dev/visualizations/)