Hi all

I am using Julia’s diffeq through R (diffeqr library) for the simulation of a simple SIR ode model. I want to interpolate a parameter value from the time in the ode model. I can set up a julia ODE model and call through R with the diffeqr library. However, I am not sure how to pass the interpolation function to the ODE? The instructions for julia suggest that any function can be introduced through the “parameter” argument of the ODE. How does this work if I call the function in R?

Below is my unsuccessfull attempt.

- julia code for the model (“juliatoymodel.jl”):

```
function model(dxdt, init , param , time)
beta, gamma, mu, sigma, eta, phi = param[1]
interpolate = param[2]
S,I,R = init
N = S + I + R
i = interpolate(time)
beta_eff = i*beta * (1.0+eta*sin(2.0*pi*(time-phi)/365.0))
FOI = beta_eff*I/N
dxdt[1] = -FOI*S + mu*N - mu*S + sigma*R
dxdt[2] = FOI*S - gamma*I - mu*I
dxdt[3] = gamma*I - mu*R - sigma*R
end
```

- R code that calls the functions:

```
library(diffeqr)
library(JuliaCall)
# params
maxtime <- 3650.0
beta <- 0.25
gamma <- 1/5
mu <- 1/(70*365)
sigma <- 1/365
eta <- 0.2
phi <- 10
theta <- c(beta, gamma, mu, sigma, eta, phi)
# init
init <- c(9999, 1, 0)
# setup environment
enviro <- diffeqr::diffeq_setup()
julia_source("juliatoymodel.jl")
# interpolation function
julia_library("Interpolations")
julia_assign("in", c(0,365,730,1095,1460,1816,2181,2546,2911,3276,3650))
julia_assign("out", c(1,1,1,1,0.9,0.8,0.7,0.8,0.9,1,1))
julia_assign("init", init)
julia_assign("param", list(theta, julia_command("interpolate = LinearInterpolation(in,out);")))
julia_assign("time", c(0.0, maxtime))
problem = julia_eval("ODEProblem(model, init, time, param)")
solution = enviro$solve(problem, enviro$AutoVern7(enviro$KenCarp4()),
saveat=7.0, abstol=1e-8, reltol=1e-6)
```

I have tried to make an R list with [[1]] params and [[2]] the interpolation function, which is assigned to a Julia object “param”. Unfortunately this throws an error

```
Error: Error happens in Julia.
MethodError: objects of type Nothing are not callable
```

because ` julia_command("interpolate = LinearInterpolation(in,out);")`

returns NULL somehow. How can I pass the interpolation function correctly? I am looking for an R/JuliaCall solution, not a pure Julia solution. Thanks a lot

Bw, Fabienne