ssm
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Inference for State Space Model (SSM)
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{
"data": [
{
"name": "all_CDC_inc_out",
"require": {"path": "data/data.csv", "fields": ["date", "all_CDC_inc_out"]}
},
{
"name": "all_google_inc_out",
"require": {"path": "data/data.csv", "fields": ["date", "all_google_inc_out"]}
},
{
"name": "paris_CDC_prev",
"require": {"path": "data/data.csv", "fields": ["date", "paris_CDC_prev"]}
},
{
"name": "nyc_CDC_inc",
"require": {"path": "data/data.csv", "fields": ["date", "nyc_CDC_inc"]}
}
],
"inputs": [
{
"name": "N_nyc",
"require": {"path": "data/N.csv", "fields": ["date", "nyc"]}
},
{
"name": "N_paris",
"require": {"path": "data/N.csv", "fields": ["date", "paris"]}
},
{
"name": "mu_b_paris",
"require": {"path": "data/mu_b.csv", "fields": ["date", "paris"]}
},
{
"name": "mu_b_nyc",
"require": {"path": "data/mu_b.csv", "fields": ["date", "nyc"]}
},
{
"name": "mu_d_paris",
"require": {"path": "data/mu_d.csv", "fields": ["date", "paris"]}
},
{
"name": "mu_d_nyc",
"require": {"path": "data/mu_d.csv", "fields": ["date", "nyc"]}
},
{
"name": "prop_all_CDC_inc",
"require": {"path": "data/prop.csv", "fields": ["date", "all_CDC_inc"]}
},
{
"name": "prop_paris_CDC_prev",
"require": {"path": "data/prop.csv", "fields": ["date", "paris_CDC_prev"]}
},
{
"name": "prop_all_google_inc",
"require": {"path": "data/prop.csv", "fields": ["date", "all_google_inc"]}
},
{
"name": "prop_nyc_CDC_inc",
"require": {"path": "data/prop.csv", "fields": ["date", "nyc_CDC_inc"]}
},
{
"name": "S_paris",
"description": "Number of susceptible",
"require": {"path": "data/pr_S_paris.json", "name": "pr_S_paris"},
"transformation": "pr_S_paris*N_paris",
"to_resource": "S_paris/N_paris"
},
{
"name": "S_nyc",
"description": "Number of susceptible",
"transformation": "pr_S_paris*N_nyc"
},
{
"name": "I_paris",
"description": "Number of infectious",
"require": {"path": "data/pr_I_paris.json", "name": "pr_I_paris"},
"transformation": "pr_I_paris*N_paris",
"to_resource": "I_paris/N_paris"
},
{
"name": "I_nyc",
"description": "Number of susceptible",
"transformation": "pr_I_paris*N_nyc"
},
{
"name": "r0_paris",
"description": "basic reproduction number",
"require": {"path": "data/r0_paris.json"}
},
{
"name": "r0_nyc",
"description": "basic reproduction number",
"require": {"path": "data/r0_nyc.json"}
},
{
"name": "v",
"description": "recovery rate",
"require": {"path": "data/pr_v.json", "name": "pr_v"},
"transformation": "1/pr_v",
"to_resource": "1/v"
},
{
"name": "sto",
"description": "noise intensity",
"require": {"path": "data/sto.json"}
},
{
"name": "rep_all_CDC_inc",
"description": "reporting rate",
"require": {"path": "data/rep_all_CDC_inc.json"}
},
{
"name": "rep_all_google_inc",
"description": "reporting rate",
"transformation": "rep_all_CDC_inc"
},
{
"name": "rep_nyc_CDC_inc",
"description": "reporting rate",
"transformation": "rep_all_CDC_inc"
},
{
"name": "rep_paris_CDC_prev",
"description": "reporting rate",
"transformation": "rep_all_CDC_inc"
},
{
"name": "phi",
"description": "over-dispertion",
"require": {"path": "data/phi.json"}
}
],
"populations": [
{"name": "paris", "composition": ["S_paris", "I_paris", "R_paris"], "remainder": {"name": "R_paris", "pop_size": "N_paris"}},
{"name": "nyc", "composition": ["S_nyc", "I_nyc", "R_nyc"], "remainder": {"name": "R_nyc", "pop_size": "N_nyc"}}
],
"reactions": [
{"from": "U", "to": "S_paris", "rate": "mu_b_paris*N_paris", "description":"birth"},
{"from": "U", "to": "S_nyc", "rate": "mu_b_nyc*N_nyc", "description":"birth"},
{"from": "S_paris", "to": "I_paris", "rate": "r0_paris/N_paris*v*I_paris", "description":"infection", "white_noise": {"name":"noise_SI", "sd": "sto"}},
{"from": "S_nyc", "to": "I_nyc", "rate": "r0_nyc/N_nyc*v*I_nyc", "description":"infection", "accumulators": ["nyc_inc"], "white_noise": {"name":"noise_SI2", "sd": "sto"}},
{"from": "I_paris", "to": "R_paris", "rate": "correct_rate(v)", "description":"recovery", "accumulators": ["all_inc_out"]},
{"from": "I_nyc", "to": "R_nyc", "rate": "correct_rate(v)", "description":"recovery", "accumulators": ["all_inc_out"]},
{"from": "S_paris", "to": "U", "rate": "mu_d_paris", "description":"death"},
{"from": "S_nyc", "to": "U", "rate": "mu_d_nyc", "description":"death"},
{"from": "I_paris", "to": "U", "rate": "mu_d_paris", "description":"death", "accumulators": ["all_inc_out"]},
{"from": "I_nyc", "to": "U", "rate": "mu_d_nyc", "description":"death", "accumulators": ["all_inc_out"]},
{"from": "R_paris", "to": "U", "rate": "mu_d_paris", "description":"death"},
{"from": "R_nyc", "to": "U", "rate": "mu_d_nyc", "description":"death"}
],
"observations": [
{
"name": "all_CDC_inc_out",
"start": "2012-07-26",
"distribution": "discretized_normal",
"mean": "rep_all_CDC_inc * prop_all_CDC_inc * all_inc_out",
"sd": "sqrt(rep_all_CDC_inc * ( 1.0 - rep_all_CDC_inc ) * prop_all_CDC_inc * all_inc_out + pow(rep_all_CDC_inc * phi * prop_all_CDC_inc * all_inc_out, 2) )"
},
{
"name": "all_google_inc_out",
"start": "2012-07-26",
"distribution": "discretized_normal",
"mean": "rep_all_google_inc * prop_all_google_inc * all_inc_out",
"sd": "sqrt(rep_all_google_inc * ( 1.0 - rep_all_google_inc ) * prop_all_google_inc * all_inc_out + pow(rep_all_google_inc * phi * prop_all_google_inc * all_inc_out, 2) )"
},
{
"name": "paris_CDC_prev",
"start": "2012-07-26",
"distribution": "discretized_normal",
"mean": "rep_paris_CDC_prev * prop_paris_CDC_prev * I_paris",
"sd": "sqrt(rep_paris_CDC_prev * ( 1.0 - rep_paris_CDC_prev ) * prop_paris_CDC_prev * I_paris + pow(rep_paris_CDC_prev * phi * prop_paris_CDC_prev * I_paris, 2) )"
},
{
"name": "nyc_CDC_inc",
"start": "2012-07-26",
"distribution": "discretized_normal",
"mean": "rep_nyc_CDC_inc * prop_nyc_CDC_inc * nyc_inc",
"sd": "sqrt(rep_nyc_CDC_inc * ( 1.0 - rep_nyc_CDC_inc ) * prop_nyc_CDC_inc * nyc_inc + pow(rep_nyc_CDC_inc * phi * prop_nyc_CDC_inc * nyc_inc, 2) )"
}
]
}