Age structured sir model for Sars-Cov-2 in Lombardia (Italy)

Andrea_Bizzotto · November 15, 2021, 2:54pm

Hi, I am new in the bayesian world. I am doing my thesis about a mathematical model that describes the epidemic of Sars-Cov-2 in Lombardaia, a region in Italy.
I would like to fit the new recovered (= hospitalized) for day.

My fitting says:

Warning messages:
1: In system(paste(CXX, ARGS), ignore.stdout = TRUE, ignore.stderr = TRUE) :
‘-E’ not found
2: There were 5999 divergent transitions after warmup. See
http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
to find out why this is a problem and how to eliminate them.
3: Examine the pairs() plot to diagnose sampling problems

4: The largest R-hat is NA, indicating chains have not mixed.
Running the chains for more iterations may help. See
http://mc-stan.org/misc/warnings.html#r-hat
5: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
Running the chains for more iterations may help. See
http://mc-stan.org/misc/warnings.html#bulk-ess
6: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
Running the chains for more iterations may help. See
http://mc-stan.org/misc/warnings.html#tail-ess

If you are interested the results, in png format, are in this link:

I don’t know how can I improve my fitting, do you have any suggestions? Thank you.

I share my code:

github.com

andbizz/thesis/blob/main/Stan_model_02.stan

//--- Stan function to obtain the distribution of the parameters in the model

//--- Define the ODE's system, whRDh a function called sir

functions{
  real[] sir(real t,       // the time t is a real variable
             real[] y,     // the vector field is made with real funtions
             real[] theta, // the parameters vector
             real[] x_r,   // these are vabiables that depend from the parameters
             int[] x_i)    // integer variables, it is used to pass the populations from parameter to input 
{ 
//--- Definition of the variables from the vector input (y) to the various componentime_sequence (S,E,I,R,H,RD)
//                                                      (x_i) to the various componentime_sequence (N_0_19,...)
//--- Group 0-19
             real S_0_19 = y[1];
             real E_0_19 = y[2];
             real I_0_19 = y[3];
             real H_0_19 = y[4];
             
             real N_0_19 = x_i[1];

This file has been truncated. show original

jsocolar · November 15, 2021, 3:02pm

I think the most important suggestion is to try to substantially simplify the model, and then build the complexity back piece-by-piece to see when the fitting issues start to appear. Perhaps the easiest simplification would be to drop some of the age classes. Does every age class run into these issues? Or are the restricted to a subset of the age classes.

Andrea_Bizzotto · November 25, 2021, 10:27am

I found the problem in the contact matrix!
Now it seems going well.
Thank you.

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Age structured sir model for Sars-Cov-2 in Lombardia (Italy)

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