Disease Transmission Modelling in Stan: The function part gives error

Modeling
1

I am new to this, while replicating the error of the code, i typed the function part and run it, it gives this outcome:

> functions {
Error: unexpected '{' in "functions {"

Please what can I do?

functions {
  real[] sir(real t, real[] y, real[] theta, 
             real[] x_r, int[] x_i) {

      real S = y[1];
      real I = y[2];
      real R = y[3];
      real N = x_i[1];
      
      real beta = theta[1];
      real sigma = theta[2];
      
      #TODO: fill it in.
      real dS_dt = 
      real dI_dt =  
      real dR_dt =  
      
      return {dS_dt, dI_dt, dR_dt};
  }
}
2

If you want to return multiple values, you first need to package them into a vector such as:
v = [dS_dt, dI_dt, dR_dt] and then return v. The use of curly brackets after return is going to result in an error. However, even if you assign the vector for dS_dt, dI_dt, and dR_dt, it will result in a new error until you complete their assignment statements (i.e. real dS_dt =, real dI_dt =, and real dR_dt =)

3

What version of Stan are you using? If I put dummy values in to the TODO section, it compiles fine with 2.30 – newer versions you probably need to rewrite the arrays from real[] to array[] real

4

Thank you for your response:
Every other lines runs:

write.csv(influenza_england_1978_school,file="mydata.csv")
library(outbreaks)
library(tidyverse)
head(influenza_england_1978_school)
theme_set(theme_bw())
ggplot(data = influenza_england_1978_school) + 
  geom_point(mapping = aes(x = date, y = in_bed)) + 
  labs(y = "Number of students in bed")
library(rstan)
library(gridExtra)
rstan_options (auto_write = TRUE)
options (mc.cores = parallel::detectCores ())

Except for this:

functions {
  real[] sir(real t, real[] y, real[] theta,
             real[] x_r, int[] x_i) {
    
    real S = y[1];
    real I = y[2];
    real R = y[3];
    real N = x_i[1];
    
    real beta = theta[1];
    real gamma = theta[2];
    
    real dS_dt = -beta * I * S / N;
    real dI_dt =  beta * I * S / N - gamma * I;
    real dR_dt =  gamma * I;
    
    return {dS_dt, dI_dt, dR_dt};
  }
}

Once I run it, it gives

> functions {
Error: unexpected '{' in "functions {"
5

I would code it like this:

functions {
  vector sir(real t , vector y, array[] real theta, array[] real x_i) {

    vector[3] dydt;
    real S = y[1];
    real I = y[2];
    real R = y[3];
    real N = x_i[1];
    
    real beta = theta[1];
    real gamma = theta[2];

    dydt[1] = -beta * I * S / N;
    dydt[2]  =  beta * I * S / N - gamma * I;
    dydt[3] =  gamma * I;

   return dydt;
  }
}

I think you’re following old code that’s not compatible with Stan’s current approach of declaring variables. For instance, real[] is not accepted anymore. It should be either vector or array[] real.

6

That looks good, but it’s faster to avoid repeating computations, so this will be more efficient:

real beta_I_S_div_N = beta * I * S / N;
real gamma_I = gamma * I;
dydt[1] = -beta_I_S_div_N;
dydt[2] = beta_I_S_divN - gamma_I;
dydt[3] = gamma_I;

It’s a lot uglier, but it saves computation. If it’s fast enough without, I wouldn’t bother.

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