How to add a known time series vector into ODE

Borrowing the ODE example from the stan documentation, I have an ODE system with one know time-dependent vector (vector Z[T] = [integers]). I know I need an interpolation function to use Z_t[i] in each step of ODE solver and use in transformed parameters as well. I have changed the code as below but cannot define the function and make it work:

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

real dydt[3];

z_t= intropolatin()
dydt[1] = -theta[1]* y[2] * y[1] ;
dydt[2] = theta[1]* y[2] * y[1] - theta[2]* y[2] + z_t;
dydt[3] =  theta[2]*  y[2];

return dydt;
data {
int<lower=1> T;
real y[T,3];
real t0;
real ts[T];
vector[T] Z;
transformed data {
int x_i[0];
real x_r[T];
for (i in 1:T){
    x_r[i] = Z[i];
transformed parameters{
  real y[T, 3];
  real cases[T - 1];
    y = integrate_ode_rk45(sir, y0, t0, ts, theta, x_r, x_i);
  for (i in 1:T-1){
   cases[i] =  y[i, 1] - y[i+1, 1] + Z[i];

Thank you in advance for your help.
#modeling #Interpolation #ODE solver #Bio