I am trying to fit an SIR model with prior distributions on the model parameters as well as on the initial value for the proportion of the population already infected (the I compartment).

```
functions {
real[] SIR(real t,
real[] y,
real[] theta,
data real[] x_r,
data 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 dSdt = -beta * S * I / N;
real dIdt = beta * S * I / N - gamma * I;
real dRdt = gamma * I;
return {dSdt, dIdt, dRdt};
}
}
data {
int<lower=0> N; // number of points
int<lower=0> n_seasons; // number of seasons
int<lower=0> seasons[N]; // seasons
real<lower=0> ili[N]; // all ili data
int<lower=0> x[N]; // week
real<lower=0> n_weeks[43];
int<lower=0> ps; // season to predict
real<lower=0,upper=1> S0; // initial susceptible proportion
real t0; // week 0
}
transformed data {
real x_r[0];
int x_i[1] = { 1 };
}
parameters {
vector[n_seasons] beta_s;
vector[n_seasons] rho_s;
real<lower=0,upper=.1> I0_s[n_seasons];
real<lower=0> epsilon;
}
transformed parameters {
vector[n_seasons] gamma_s;
for (i in 1:n_seasons) {
gamma_s[i] = beta_s[i] * rho_s[i];
R0 = 1 - S0 - I0_s[i];
}
}
model {
for (i in 1:n_seasons) {
beta_s[i] ~ gamma(2,.02);
rho_s[i] ~ gamma(2,.02);
I0_s[i] ~ normal(.05,.02);
}
epsilon ~ exponential(100);
for (i in 1:N) {
ili[i] ~ normal(col(to_matrix(integrate_ode_rk45(SIR,
{S0, I0_s[seasons[i]], 1 - S0 - I0_s[seasons[i]]},
t0, n_weeks,
{beta_s[seasons[i]], gamma_s[seasons[i]]},
x_r, x_i)),2),
epsilon);
}
}
```

I run the model in R using `rstan`

and I get the following error

```
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: loop iteration: 1
Chain 1: Unrecoverable error evaluating the log probability at the initial value.
Chain 1: Exception: Max number of iterations exceeded (1000000). (in 'model27678c0a492_af4cfd756eb609d1cf3b6b499e742e03' at line 96)
[1] "Error in sampler$call_sampler(args_list[[i]]) : "
[2] " Exception: Max number of iterations exceeded (1000000). (in 'model27678c0a492_af4cfd756eb609d1cf3b6b499e742e03' at line 96)"
error occurred during calling the sampler; sampling not done
```

I’m very lost trying to figure this one out. Any ideas what I might be doing wrong? Also included is the code for the data list I’m using in R, as well as a .csv

file of my data.

ILINet_samp.csv (19.1 KB)

```
dat = list(N = nrow(ILINet_samp),
n_seasons = length(unique(ILINet_samp$season)),
seasons = as.numeric(factor(ILINet_samp$season)),
ili = ILINet_samp$unweighted_ili/100,
x = ILINet_samp$season_week,
# n_weeks = ILINet_samp$n_weeks,
n_weeks = 1:43,
ps = max(as.numeric(factor(unique(ILINet_samp$season)))),
S0 = .9,
t0 = 0)
```