# Estimating parameters of a SEIR model

The problem is with the model formulation.

The Poisson and binomial are defined on integers. If you want to use non-integers as your data, you’ll need to use a different likelihood.

So there is a way to overcome this and that is in the level of ODEs, everywhere there is S we divide by N which is the population N was 1 now we put the real value for it so 66500000. I have made the following modifications:

On the R side I defined `n <- 66500000`

then on the stan side I have done the following on the function block:

``````functions {

real[] SI(real t,
real[] y,
real[] params,
real[] x_r,
int[] x_i) {

real dydt;

// Variables of the ODEs

real S = y;
real E = y;
real G = y;
real P = y;
real I = y;
real A = y;
real B = y;
real C = y;

// The parameters of the ODEs
real phi = params;
real pe = params;
real pie = params;
real pee = params;

real beta = params;
real mu = params;
real betam = params;
real tau = params;
real alpha = params;
real Ts = params;
real Ta = params;
real Tm = params;
real Ti = params;

dydt = - (mu * beta * S * A - beta * S * I - beta * C * S - betam * B * S) / n;
dydt = (mu * beta * S * A + (1 - phi) * beta * S * I + (1 - phi) * beta * C * S + (1 - phi) * betam * B * S)/n - E / tau;
dydt = (pe * phi * beta * S * I + pie * phi * beta * C * S + pee * phi * betam * B * S)/n - G / tau;
dydt = ((1 - pe) * phi * beta * S * I + (1 - pie) * phi * beta * C * S + (1 - pee) * phi * betam * B * S)/n - P / tau;
dydt = alpha * E / tau - I / Ts;
dydt = (1 - alpha) * E / tau - A / Ta;
dydt = G / tau - B / Tm;
dydt = P / tau - C / Ti;

return dydt;
}

}
``````

the first 4 ODEs have S so I divide them accordingly by `n`. Then in data block I added the following:

``````data {
int<lower = 0, upper = 66500000> n //population
...
}
``````

where `...` means the rest are the same. Is this correct way of adding the parameter `n`?

Then in parameter block I commented out the part I have ` //real<lower = 0, upper = 1> S0; // Initial fraction of susceptible` and in transformed parameter block I modified the initial conditions as:

``````transformed parameters{
...
y0 = (1 - 0.02 - 0.001)*66500000;
y0 = 0.02*66500000;
y0 = 0;
y0 = 0;
y0 = 0.001*66500000;
y0 = 0;
y0 = 0;
y0 = 0;
...

}
``````

now in

``````stan_d = list(n_obs = length(datalist\$cases),
n_params = 13,
n_difeq = 8,
y = datalist\$cases,
t0 = 0,
ts = sample_time)
``````

`y` are integers. My full R + stan code is:

``````library(tidyverse)
library(deSolve)
library(dplyr)
library(ggplot2)
library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())

ggplot(data = datalist) +
geom_point(mapping = aes(x = date, y = cases)) +
labs(y = "Number of daily cases")

sample_time = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70,
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116)
n <- 66500000

# The Stan model statement:
cat(
'
functions {

real[] SI(real t,
real[] y,
real[] params,
real[] x_r,
int[] x_i) {

real dydt;

// Variables of the ODEs

real S = y;
real E = y;
real G = y;
real P = y;
real I = y;
real A = y;
real B = y;
real C = y;

// The parameters of the ODEs
real phi = params;
real pe = params;
real pie = params;
real pee = params;

real beta = params;
real mu = params;
real betam = params;
real tau = params;
real alpha = params;
real Ts = params;
real Ta = params;
real Tm = params;
real Ti = params;

dydt = - (mu * beta * S * A - beta * S * I - beta * C * S - betam * B * S) / n;
dydt = (mu * beta * S * A + (1 - phi) * beta * S * I + (1 - phi) * beta * C * S + (1 - phi) * betam * B * S)/n - E / tau;
dydt = (pe * phi * beta * S * I + pie * phi * beta * C * S + pee * phi * betam * B * S)/n - G / tau;
dydt = ((1 - pe) * phi * beta * S * I + (1 - pie) * phi * beta * C * S + (1 - pee) * phi * betam * B * S)/n - P / tau;
dydt = alpha * E / tau - I / Ts;
dydt = (1 - alpha) * E / tau - A / Ta;
dydt = G / tau - B / Tm;
dydt = P / tau - C / Ti;

return dydt;
}

}

data {
int<lower = 0, upper = 66500000> n //population
int<lower = 1> n_obs; // Number of days sampled
int<lower = 1> n_params; // Number of model parameters
int<lower = 1> n_difeq; // Number of differential equations in the system
//int<lower = 1> n_sample;
int y[n_obs]; // The binomially distributed data
real t0; // Initial time point (zero)
real ts[n_obs]; // Time points that were sampled

}

transformed data {
real x_r;
int x_i;
}

parameters {
real<lower = 0, upper = 1> phi;
real<lower = 0, upper = 1> pe;
real<lower = 0, upper = 1> pie;
real<lower = 0, upper = 1> pee;
real<lower = 0> beta;
real<lower = 0> mu;
real<lower = 0>betam;
real<lower = 0> tau;
real<lower = 0> alpha;
real<lower = 0> Ts;
real<lower = 0> Ta;
real<lower = 0> Tm;
real<lower = 0> Ti;
//real<lower = 0, upper = 1> S0; // Initial fraction of susceptible
}

transformed parameters{
real y_hat[n_obs, n_difeq]; // Output from the ODE solver
real y0[n_difeq]; // Initial conditions
real<lower=0, upper=1> params1;
real<lower = 0> params2;

y0 = (1 - 0.02 - 0.001)*66500000;
y0 = 0.02*66500000;
y0 = 0;
y0 = 0;
y0 = 0.001*66500000;
y0 = 0;
y0 = 0;
y0 = 0;

y_hat = integrate_ode_rk45(SI, y0, t0, ts, {phi, pe, pie, pee, beta, mu, betam, tau, alpha, Ts, Ta, Tm, Ti}, x_r, x_i);
//for(i in 1:n_obs){
//for(j in 1:n_difeq){
//y_hat[i, j] = 1e-6 + (1-2e-6)*y_hat[i, j];
//}
//}

}

model {
phi ~ normal(0, 1);  //phi
pe ~ normal(0, 1); //pe
pie ~ normal(0, 1); //pie
pee ~ normal(0, 1); //pee

beta ~ normal(0.5, 0.9); //beta
mu ~ normal(0.2, 0.55); //mu
betam ~ normal(0, 1);  //beta_m
tau ~ normal(1, 20); //tau
alpha ~ normal(0.1, 0.99); //alpha
Ts ~ normal(3, 20); //Ts
Ta ~ normal(1, 20); //Ta
Tm ~ normal(1, 20); //Tm
Ti ~ normal(0.5, 8); //Ti
//S0 ~ normal(0.5, 0.5); //constrained to be 0-1.

y ~ poisson(y_hat[,5]); //y_hat[,5] are the fractions infected from the ODE solver
}

generated quantities {
real R_0;
R_0 = beta * Ta * (alpha * Ts * (1 - phi) / Ta + mu * (1 - alpha));

}

',
file = "SI_fit.stan", sep="", fill=T)

# FITTING

# For stan model we need the following variables:

stan_d = list(n_obs = length(datalist\$cases),
n_params = 13,
n_difeq = 8,
y = datalist\$cases,
t0 = 0,
ts = sample_time)

# Which parameters to monitor in the model:
params_monitor = c("y_hat", "y0", "params", "R_0")

# Test / debug the model:
test = stan("SI_fit.stan",
data = stan_d,
pars = params_monitor,
chains = 1, iter = 10)

# Fit and sample from the posterior

#mod = stan(fit = test,
#           data = stan_d,
#           pars = params_monitor,
#           chains = 3,
#           warmup = 500,
#           iter = 1000,
#           control = list(adapt_delta = 0.99))
mod = stan(fit = test,
data = stan_d,
pars = params_monitor,
chains = 3,
warmup = 500,
iter = 1000)

# You should do some MCMC diagnostics, including:
#traceplot(mod, pars="lp__")
#traceplot(mod, pars=c("params", "y0"))
#summary(mod)\$summary[,"Rhat"]

# Extract the posterior samples to a structured list:
posts <- extract(mod)
``````

which is not running, I wonder if the problem is because I have defined `n` on R side, or wether I made a mistake defining it on stan? namely my modification in data block. If I can do this everything would be integer and I should be able to run the naive likelihood I imagine.

I think your best bet is to look at the case study here and think through how they’ve defined everything: https://mc-stan.org/users/documentation/case-studies/boarding_school_case_study.html . Their data is in total number of people infected and they’re modeling this with an SIR model.

Think about what are the units for `I(t)`? And what are the units for `y[t]`? Are they integers representing numbers of people? Or are they real numbers representing millions of people? Or are they real numbers representing some fraction of 66.5 million people?

1 Like

First of all I reconstructed the model given by the link you have shared and I got exactly as they have the code for that is (I am adding this not to lose generality as their stan file is separated whereas mine is included in the same file and it works just fine):

``````library(outbreaks)
library(tidyverse)
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 ())
set.seed(3) # for reproductibility

cat(
'
functions {
real[] sir(real t, real[] y, real[] theta,
real[] x_r, int[] x_i) {

real S = y;
real I = y;
real R = y;
real N = x_i;

real beta = theta;
real gamma = theta;

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};
}
}
data {
int<lower=1> n_days;
real y0;
real t0;
real ts[n_days];
int N;
int cases[n_days];
}
transformed data {
real x_r;
int x_i = { N };
}
parameters {
real<lower=0> gamma;
real<lower=0> beta;
real<lower=0> phi_inv;
}
transformed parameters{
real y[n_days, 3];
real phi = 1. / phi_inv;
{
real theta;
theta = beta;
theta = gamma;

y = integrate_ode_rk45(sir, y0, t0, ts, theta, x_r, x_i);
}
}
model {
//priors
beta ~ normal(2, 1);
gamma ~ normal(0.4, 0.5);
phi_inv ~ exponential(5);

//sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_2(col(to_matrix(y), 2), phi);
}
generated quantities {
real R0 = beta / gamma;
real recovery_time = 1 / gamma;
real pred_cases[n_days];
pred_cases = neg_binomial_2_rng(col(to_matrix(y), 2), phi);
}
',
file = "sir_negbin.stan", sep="", fill=T)

# time series of cases
cases <- influenza_england_1978_school\$in_bed  # Number of students in bed
# total count
N <- 763;
# times
n_days <- length(cases)
t <- seq(0, n_days, by = 1)
t0 = 0
t <- t[-1]
#initial conditions
i0 <- 1
s0 <- N - i0
r0 <- 0
y0 = c(S = s0, I = i0, R = r0)
# data for Stan
data_sir <- list(n_days = n_days, y0 = y0, t0 = t0, ts = t, N = N, cases = cases)
# number of MCMC steps
niter <- 2000

model <- stan_model("sir_negbin.stan")

fit_sir_negbin <- sampling(model,
data = data_sir,
iter = niter,
chains = 4)

pars=c('beta', 'gamma', "R0", "recovery_time")

print(fit_sir_negbin, pars = pars)

stan_dens(fit_sir_negbin, pars = pars, separate_chains = TRUE)
``````

In the next step I did a naive modelling, namely I imported my data instead of the influenza’s to just check wether the model would run, it did indeed while the fit was not good (at least I know my data is workable). The code for that is as follow:

``````library(ggplot2)
ggplot(data = datalist) +
geom_point(mapping = aes(x = day, y = cases0)) +
labs(y = "Number of daily infected people")

library(rstan)
library(gridExtra)
rstan_options (auto_write = TRUE)
options (mc.cores = parallel::detectCores ())
set.seed(3) # for reproductibility

cat(
'
functions {
real[] sir(real t, real[] y, real[] theta,
real[] x_r, int[] x_i) {

real S = y;
real I = y;
real R = y;
real N = x_i;

real beta = theta;
real gamma = theta;

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};
}
}
data {
int<lower=1> n_days;
real y0;
real t0;
real ts[n_days];
int N;
int cases[n_days];
}
transformed data {
real x_r;
int x_i = { N };
}
parameters {
real<lower=0> gamma;
real<lower=0> beta;
real<lower=0> phi_inv;
}
transformed parameters{
real y[n_days, 3];
real phi = 1. / phi_inv;
{
real theta;
theta = beta;
theta = gamma;

y = integrate_ode_rk45(sir, y0, t0, ts, theta, x_r, x_i);
}
}
model {
//priors
beta ~ normal(2, 1);
gamma ~ normal(0.4, 0.5);
phi_inv ~ exponential(5);

//sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_2(col(to_matrix(y), 2), phi);
}
generated quantities {
real R0 = beta / gamma;
real recovery_time = 1 / gamma;
real pred_cases[n_days];
pred_cases = neg_binomial_2_rng(col(to_matrix(y), 2), phi);
}
',
file = "sir_negbin.stan", sep="", fill=T)

# time series of cases
cases <- datalist\$cases0  # Number of students in bed
# total count
N <- 66500000;
# times
n_days <- length(cases)
t <- seq(0, n_days, by = 1)
t0 = 0
t <- t[-1]
#initial conditions
i0 <- 1
s0 <- N - i0
r0 <- 0
y0 = c(S = s0, I = i0, R = r0)
# data for Stan
data_sir <- list(n_days = n_days, y0 = y0, t0 = t0, ts = t, N = N, cases = cases)
# number of MCMC steps
niter <- 2000

model <- stan_model("sir_negbin.stan")

fit_sir_negbin <- sampling(model,
data = data_sir,
iter = niter,
chains = 4)

pars=c('beta', 'gamma', "R0", "recovery_time")

print(fit_sir_negbin, pars = pars)

stan_dens(fit_sir_negbin, pars = pars, separate_chains = TRUE)

smr_pred <- cbind(as.data.frame(summary(
fit_sir_negbin, pars = "pred_cases", probs = c(0.05, 0.5, 0.95))\$summary), t, cases)
colnames(smr_pred) <- make.names(colnames(smr_pred)) # to remove % in the col names

ggplot(smr_pred, mapping = aes(x = t)) +
geom_ribbon(aes(ymin = X5., ymax = X95.), fill = "orange", alpha = 0.6) +
geom_line(mapping = aes(x = t, y = X50.)) +
geom_point(mapping = aes(y = cases)) +
labs(x = "Day", y = "Number of daily infected people")
``````

The data is here: xyzz.csv (2.1 KB) and you can see from the last part of the code that the fit is not great but as I mentioned thankfully it works. In the final step I went line by line and in similar manner employed my model:

``````library(ggplot2)
ggplot(data = datalist) +
geom_point(mapping = aes(x = day, y = cases0)) +
labs(y = "Number of daily infected people")

library(rstan)
library(gridExtra)
rstan_options (auto_write = TRUE)
options (mc.cores = parallel::detectCores ())
set.seed(3) # for reproductibility

cat(
'
functions {
real[] sir(real t, real[] y, real[] theta,
real[] x_r, int[] x_i) {

real S = y;
real E = y;
real G = y;
real P = y;
real I = y;
real A = y;
real B = y;
real C = y;
real N = x_i;

real phi = theta;
real pe = theta;
real pie = theta;
real pee = theta;
real beta = theta;
real mu = theta;
real betam = theta;
real tau = theta;
real alpha = theta;
real Ts = theta;
real Ta = theta;
real Tm = theta;
real Ti = theta;

real dS_dt = - mu * beta * S / N * A - beta * S / N * I - beta * C * S / N - betam * B * S / N;
real dE_dt = mu * beta * S / N * A + (1 - phi) * beta * S / N * I + (1 - phi) * beta * C * S / N + (1 - phi) * betam * B * S / N - E / tau;
real dG_dt = pe * phi * beta * S / N * I + pie * phi * beta * C * S / N + pee * phi * betam * B * S / N - G / tau;
real dP_dt = (1 - pe) * phi * beta * S / N * I + (1 - pie) * phi * beta * C * S / N + (1 - pee) * phi * betam * B * S / N - P / tau;
real dI_dt = alpha * E / tau - I / Ts;
real dA_dt = (1 - alpha) * E / tau - A / Ta;
real dB_dt = G / tau - B / Tm;
real dC_dt = P / tau - C / Ti;

return {dS_dt, dE_dt, dG_dt, dP_dt, dI_dt, dA_dt, dB_dt, dC_dt};
}
}
data {
int<lower=1> n_days;
real y0;
real t0;
real ts[n_days];
int N;
int cases[n_days];
}
transformed data {
real x_r;
int x_i = { N };
}
parameters {
real<lower = 0, upper = 1> phi;
real<lower = 0, upper = 1> pe;
real<lower = 0, upper = 1> pie;
real<lower = 0, upper = 1> pee;
real<lower = 0> beta;
real<lower = 0> mu;
real<lower = 0> betam;
real<lower = 0> tau;
real<lower = 0> alpha;
real<lower = 0> Ts;
real<lower = 0> Ta;
real<lower = 0> Tm;
real<lower = 0> Ti;
real<lower=0> phi_inv;
}
transformed parameters{
real y[n_days, 8];
real phi = 1. / phi_inv;
{
real theta;
theta = phi;
theta = pe;
theta = pie;
theta = pee;
theta = beta;
theta = mu;
theta = betam;
theta = tau;
theta = alpha;
theta = Ts;
theta = Ta;
theta = Tm;
theta = Ti;

y = integrate_ode_rk45(sir, y0, t0, ts, theta, x_r, x_i);
}
}
model {
//priors
phi ~ normal(0, 1);
pe ~ normal(0, 1);
pie ~ normal(0, 1);
pee ~ normal(0, 1);
beta ~ normal(0.5, 0.9);
mu ~ normal(0.2, 0.55);
betam ~ normal(0, 1);
tau ~ normal(1, 20);
alpha ~ normal(0.1, 0.99);
Ts ~ normal(3, 20);
Ta ~ normal(1, 20);
Tm ~ normal(1, 20);
Ti ~ normal(0.5, 8);
phi_inv ~ exponential(5);

//sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_5(col(to_matrix(y), 5), phi);
}
generated quantities {
real R0 = beta * Ta * (alpha * Ts * (1 - phi) / Ta + mu * (1 - alpha));
real pred_cases[n_days];
pred_cases = neg_binomial_5_rng(col(to_matrix(y), 5), phi);
}

',
file = "sir_negbin.stan", sep="", fill=T)

# time series of cases
cases <- datalist\$cases0  # Number of students in bed
# total count
N <- 66500000;
# times
n_days <- length(cases)
t <- seq(0, n_days, by = 1)
t0 = 0
t <- t[-1]
#initial conditions
i0 <- N / 10000
s0 <- N
e0 <- N / 1000
g0 <- 0
p0 <- 0
a0 <- N / 100000
b0 <- 0
c0 <- 0

y0 = c(S = s0, E = e0, G = g0, P = p0, I = i0, A = a0, B = b0, C = c0)
# data for Stan
data_sir <- list(n_days = n_days, y0 = y0, t0 = t0, ts = t, N = N, cases = cases)
# number of MCMC steps
niter <- 2000

model <- stan_model("sir_negbin.stan")

fit_sir_negbin <- sampling(model,
data = data_sir,
iter = niter,
chains = 4)

pars=c('phi', 'pe', "pie", "pee", "beta", "mu", "betam", "tau", "alpha", "Ts", "Ta", "Tm", "Ta", "R0")

print(fit_sir_negbin, pars = pars)

stan_dens(fit_sir_negbin, pars = pars, separate_chains = TRUE)

smr_pred <- cbind(as.data.frame(summary(
fit_sir_negbin, pars = "pred_cases", probs = c(0.05, 0.5, 0.95))\$summary), t, cases)
colnames(smr_pred) <- make.names(colnames(smr_pred)) # to remove % in the col names

ggplot(smr_pred, mapping = aes(x = t)) +
geom_ribbon(aes(ymin = X5., ymax = X95.), fill = "orange", alpha = 0.6) +
geom_line(mapping = aes(x = t, y = X50.)) +
geom_point(mapping = aes(y = cases)) +
labs(x = "Day", y = "Number of daily infected people")
``````

Now let me go through it, I have 8 ODEs with the dI_dt being the infected ones and the rest are other compartments. `dI_dt` is the 5th ODE so accordingly in `model{}` block I have:

``````  //sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_5(col(to_matrix(y), 5), phi);
``````

where you see 5 as index for the infected compartment. This was

`````` cases ~ neg_binomial_2(col(to_matrix(y), 2), phi);
``````

for the original model as `I(t)` was the second ODE. In this model I am following the logic of the link in terms of defining the population i.e. `N = S+E+G+P+I+A+B+C` I have also defined the initial conditions accordingly. Yet when I run this it stops at the level of compiling the model namely

``````model <- stan_model("sir_negbin.stan")
``````

I know that the likelihood might not be correct but I wonder why does the code not get compiled. I appreciate your help.

Thanks for the script. This is the error that I’m getting when I go to compile the last model:

``````SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Duplicate declaration of variable, name=phi; attempt to redeclare as real in transformed parameter; previously declared as real in parameter
error in 'model668664f0eb3f_sir_negbin' at line 74, column 25
-------------------------------------------------
72: transformed parameters{
73:   real y[n_days, 8];
74:   real phi = 1. / phi_inv;
^
75:   {
-------------------------------------------------

Error in stanc(file = file, model_code = model_code, model_name = model_name,  :
failed to parse Stan model 'sir_negbin' due to the above error.
``````

Out of curiosity, are you getting this error? Or is rstan giving you something else? If it’s giving you something else, what operating system are you using?

1 Like

I was getting the

``````Error in close.connection(zz)
``````

But from your run I think the problem was at line `74 real phi` as I have had `phi` as parameter of ODE, so I changed the name of it to `phi`. The full code is:

``````library(ggplot2)
ggplot(data = datalist) +
geom_point(mapping = aes(x = day, y = cases0)) +
labs(y = "Number of daily infected people")

library(rstan)
library(gridExtra)
rstan_options (auto_write = TRUE)
options (mc.cores = parallel::detectCores ())
set.seed(3) # for reproductibility

cat(
'
functions {
real[] sir(real t, real[] y, real[] theta,
real[] x_r, int[] x_i) {

real S = y;
real E = y;
real G = y;
real P = y;
real I = y;
real A = y;
real B = y;
real C = y;
real N = x_i;

real phi = theta;
real pe = theta;
real pie = theta;
real pee = theta;
real beta = theta;
real mu = theta;
real betam = theta;
real tau = theta;
real alpha = theta;
real Ts = theta;
real Ta = theta;
real Tm = theta;
real Ti = theta;

real dS_dt = - mu * beta * S / N * A - beta * S / N * I - beta * C * S / N - betam * B * S / N;
real dE_dt = mu * beta * S / N * A + (1 - phi) * beta * S / N * I + (1 - phi) * beta * C * S / N + (1 - phi) * betam * B * S / N - E / tau;
real dG_dt = pe * phi * beta * S / N * I + pie * phi * beta * C * S / N + pee * phi * betam * B * S / N - G / tau;
real dP_dt = (1 - pe) * phi * beta * S / N * I + (1 - pie) * phi * beta * C * S / N + (1 - pee) * phi * betam * B * S / N - P / tau;
real dI_dt = alpha * E / tau - I / Ts;
real dA_dt = (1 - alpha) * E / tau - A / Ta;
real dB_dt = G / tau - B / Tm;
real dC_dt = P / tau - C / Ti;

return {dS_dt, dE_dt, dG_dt, dP_dt, dI_dt, dA_dt, dB_dt, dC_dt};
}
}
data {
int<lower=1> n_days;
real y0;
real t0;
real ts[n_days];
int N;
int cases[n_days];
}
transformed data {
real x_r;
int x_i = { N };
}
parameters {
real<lower = 0, upper = 1> phi;
real<lower = 0, upper = 1> pe;
real<lower = 0, upper = 1> pie;
real<lower = 0, upper = 1> pee;
real<lower = 0> beta;
real<lower = 0> mu;
real<lower = 0> betam;
real<lower = 0> tau;
real<lower = 0> alpha;
real<lower = 0> Ts;
real<lower = 0> Ta;
real<lower = 0> Tm;
real<lower = 0> Ti;
real<lower=0> phi_inv;
}
transformed parameters{
real y[n_days, 8];
real phii = 1. / phi_inv;
{
real theta;
theta = phi;
theta = pe;
theta = pie;
theta = pee;
theta = beta;
theta = mu;
theta = betam;
theta = tau;
theta = alpha;
theta = Ts;
theta = Ta;
theta = Tm;
theta = Ti;

y = integrate_ode_rk45(sir, y0, t0, ts, theta, x_r, x_i);
}
}
model {
//priors
phi ~ normal(0, 1);
pe ~ normal(0, 1);
pie ~ normal(0, 1);
pee ~ normal(0, 1);
beta ~ normal(0.5, 0.9);
mu ~ normal(0.2, 0.55);
betam ~ normal(0, 1);
tau ~ normal(1, 20);
alpha ~ normal(0.1, 0.99);
Ts ~ normal(3, 20);
Ta ~ normal(1, 20);
Tm ~ normal(1, 20);
Ti ~ normal(0.5, 8);
phi_inv ~ exponential(5);

//sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_5(col(to_matrix(y), 5), phii);
}
generated quantities {
real R0 = beta * Ta * (alpha * Ts * (1 - phi) / Ta + mu * (1 - alpha));
real pred_cases[n_days];
pred_cases = neg_binomial_5_rng(col(to_matrix(y), 5), phii);
}

',
file = "sir_negbin.stan", sep="", fill=T)

# time series of cases
cases <- datalist\$cases0  # Number of students in bed
# total count
N <- 66500000;
# times
n_days <- length(cases)
t <- seq(0, n_days, by = 1)
t0 = 0
t <- t[-1]
#initial conditions
i0 <- N / 10000
s0 <- N
e0 <- N / 1000
g0 <- 0
p0 <- 0
a0 <- N / 100000
b0 <- 0
c0 <- 0

y0 = c(S = s0, E = e0, G = g0, P = p0, I = i0, A = a0, B = b0, C = c0)
# data for Stan
data_sir <- list(n_days = n_days, y0 = y0, t0 = t0, ts = t, N = N, cases = cases)
# number of MCMC steps
niter <- 2000

model <- stan_model("sir_negbin.stan")

fit_sir_negbin <- sampling(model,
data = data_sir,
iter = niter,
chains = 4)

pars=c('phi', 'pe', "pie", "pee", "beta", "mu", "betam", "tau", "alpha", "Ts", "Ta", "Tm", "Ta", "R0")

print(fit_sir_negbin, pars = pars)

stan_dens(fit_sir_negbin, pars = pars, separate_chains = TRUE)

smr_pred <- cbind(as.data.frame(summary(
fit_sir_negbin, pars = "pred_cases", probs = c(0.05, 0.5, 0.95))\$summary), t, cases)
colnames(smr_pred) <- make.names(colnames(smr_pred)) # to remove % in the col names

ggplot(smr_pred, mapping = aes(x = t)) +
geom_ribbon(aes(ymin = X5., ymax = X95.), fill = "orange", alpha = 0.6) +
geom_line(mapping = aes(x = t, y = X50.)) +
geom_point(mapping = aes(y = cases)) +
labs(x = "Day", y = "Number of daily infected people")
``````

where now in transformed parameter block we have `real phii = 1. / phi_inv;` subsequently, in model block we have:

`````` cases ~ neg_binomial_5(col(to_matrix(y), 5), phii);
``````

and in generated quantities:

``````pred_cases = neg_binomial_5_rng(col(to_matrix(y), 5), phii);
``````

yet it is not compiling unfortunately. I really appreciate your time and help on this @bbbales2.

It’s neg_binomial_2, not neg_binomial_5 is the thing:

``````...
model {
//priors
phi ~ normal(0, 1);
pe ~ normal(0, 1);
pie ~ normal(0, 1);
pee ~ normal(0, 1);
beta ~ normal(0.5, 0.9);
mu ~ normal(0.2, 0.55);
betam ~ normal(0, 1);
tau ~ normal(1, 20);
alpha ~ normal(0.1, 0.99);
Ts ~ normal(3, 20);
Ta ~ normal(1, 20);
Tm ~ normal(1, 20);
Ti ~ normal(0.5, 8);
phi_inv ~ exponential(5);

//sampling distribution
//col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
cases ~ neg_binomial_2(col(to_matrix(y), 5), phii);
}
generated quantities {
real R0 = beta * Ta * (alpha * Ts * (1 - phi) / Ta + mu * (1 - alpha));
real pred_cases[n_days];
pred_cases = neg_binomial_2_rng(col(to_matrix(y), 5), phii);
}
``````

With this the model compiles for me.

I feel like your rstan is not working correctly.

You shouldn’t be getting error messages like this:

``````Error in close.connection(zz)
``````

You should be getting error messages like:

``````SYNTAX ERROR, MESSAGE(S) FROM PARSER:
Probability function must end in _lpdf or _lpmf. Found distribution family = neg_binomial_5 with no corresponding probability function neg_binomial_5_lpdf, neg_binomial_5_lpmf, or neg_binomial_5_log
error in 'model66865f3d2989_sir_negbin' at line 113, column 53
-------------------------------------------------
111:   //sampling distribution
112:   //col(matrix x, int n) - The n-th column of matrix x. Here the number of infected people
113:   cases ~ neg_binomial_5(col(to_matrix(y), 5), phii);
^
114: }
-------------------------------------------------

Error in stanc(file = file, model_code = model_code, model_name = model_name,  :
failed to parse Stan model 'sir_negbin' due to the above error.
``````

If you can, maybe try installing cmdstanr and switch to it? It is an alternative interface to Stan for R: https://mc-stan.org/cmdstanr/

If nothing else, maybe upgrade to R 4.0 and see if things start working? Only do that if you can risk other packages breaking though: R 4.0, rstan, and you

What operating system are you using? Is this Catalina? Or something else?

2 Likes

Thank you so much for this. I can now compile too. Before employing your suggestion I have a question:
To install cmdstanr do I need to remove rstan using `remove.packages("rstan")` first?

I use Catalina unfortunately which I know has some conflicts with basically everything.

Also do you get `SYNTAX ERROR, MESSAGE(S) FROM PARSER` by `cmdstanr` or `rstan`? indeed this should help me as the connection error, as you also mentioned, helps nothing at all and I am troubleshooting in the dark basically.

May as well. I have both installed and they work fine side by side for me though. Your mileage may vary.

Those errors I posted were from rstan, but cmdstanr should give equivalent ones.

Yeah debugging these models without syntax errors would be just impossible.