{
  "id": "seirhd-stockflow",
  "header": {
    "name": "SEIRHD Model",
    "schema": "https://raw.githubusercontent.com/DARPA-ASKEM/Model-Representations/stockflow_v0.1/stockflow/stockflow_schema.json",
    "description": "SEIRHD model",
    "schema_name": "stockflow",
    "model_version": "0.1"
  },
  "model": {
    "flows": [
      {
        "id": "flow1",
        "name": "NewExposed",
        "upstream_stock": "S",
        "downstream_stock": "E",
        "rate_expression": "cbeta * S * I / N",
        "rate_expression_mathml": "<apply><divide/><apply><times/><ci>I</ci><ci>S</ci><ci>cbeta</ci></apply><ci>N</ci></apply>"
      },
      {
        "id": "flow2",
        "name": "NewInfected",
        "upstream_stock": "E",
        "downstream_stock": "I",
        "rate_expression": "E*cdelta",
        "rate_expression_mathml": "<apply><times/><ci>E</ci><ci>cdelta</ci></apply>"
      },
      {
        "id": "flow3",
        "name": "NewHosp",
        "upstream_stock": "I",
        "downstream_stock": "H",
        "rate_expression": "I*cgamma*hosp",
        "rate_expression_mathml": "<apply><times/><ci>I</ci><ci>cgamma</ci><ci>hosp</ci></apply>"
      },
      {
        "id": "flow4",
        "name": "NewRecovery",
        "upstream_stock": "I",
        "downstream_stock": "R",
        "rate_expression": "I*cgamma*(1 - hosp)",
        "rate_expression_mathml": "<apply><times/><ci>I</ci><ci>cgamma</ci><apply><minus/><cn>1</cn><ci>hosp</ci></apply></apply>"
      },
      {
        "id": "flow5",
        "name": "NewRecoveryFromHosp",
        "upstream_stock": "H",
        "downstream_stock": "R",
        "rate_expression": "(1 - death) * H / los",
        "rate_expression_mathml": "<apply><divide/><apply><times/> <apply><minus/><cn>1</cn><ci>death</ci></apply><ci>H</ci></apply><ci>los</ci></apply>"
      },
      {
        "id": "flow6",
        "name": "NewDeath",
        "upstream_stock": "H",
        "downstream_stock": "D",
        "rate_expression": "death * H / los",
        "rate_expression_mathml": "<apply><divide/><apply><times/><ci>death</ci><ci>H</ci></apply><ci>los</ci></apply>"
      }
    ],
    "stocks": [
      {
        "id": "S",
        "name": "Susceptible",
        "grounding": {
          "identifiers": {
            "ido": "0000514"
          }
        }
      },
      {
        "id": "E",
        "name": "Exposed"
      },
      {
        "id": "I",
        "name": "Infected"
      },
      {
        "id": "R",
        "name": "Recovered"
      },
      {
        "id": "H",
        "name": "Hospitalized"
      },
      {
        "id": "D",
        "name": "Deceased"
      }
    ],
    "auxiliaries": [
      {
        "id": "cbeta",
        "name": "cbeta",
        "expression": "1.0 * p_cbeta",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_cbeta</ci></apply>"
      },
      {
        "id": "cdelta",
        "name": "cdelta",
        "expression": "1.0 * p_cdelta",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_cdelta</ci></apply>"
      },
      {
        "id": "N",
        "name": "N",
        "expression": "1.0 * p_N",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_N</ci></apply>"
      },
      {
        "id": "death",
        "name": "death",
        "expression": "1.0 * p_death",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_death</ci></apply>"
      },
      {
        "id": "hosp",
        "name": "hosp",
        "expression": "1.0 * p_hosp",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_hosp</ci></apply>"
      },
      {
        "id": "los",
        "name": "los",
        "expression": "1.0 * p_los",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_los</ci></apply>"
      },
      {
        "id": "cgamma",
        "name": "cgamma",
        "expression": "1.0 * p_cgamma",
        "expression_mathml": "<apply><times/><cn>1.0</cn><ci>p_cgamma</ci></apply>"
      }
    ],
    "links": [
      {
        "id": "link1",
        "source": "S",
        "target": "flow1"
      },
      {
        "id": "link2",
        "source": "E",
        "target": "flow1"
      },
      {
        "id": "link3",
        "source": "I",
        "target": "flow1"
      },
      {
        "id": "link4",
        "source": "cbeta",
        "target": "flow1"
      },
      {
        "id": "link5",
        "source": "N",
        "target": "flow1"
      },
      {
        "id": "link6",
        "source": "E",
        "target": "flow2"
      },
      {
        "id": "link7",
        "source": "I",
        "target": "flow2"
      },
      {
        "id": "link8",
        "source": "cdelta",
        "target": "flow2"
      },
      {
        "id": "link9",
        "source": "I",
        "target": "flow3"
      },
      {
        "id": "link10",
        "source": "H",
        "target": "flow3"
      },
      {
        "id": "link11",
        "source": "cgamma",
        "target": "flow3"
      },
      {
        "id": "link12",
        "source": "hosp",
        "target": "flow3"
      },
      {
        "id": "link13",
        "source": "I",
        "target": "flow4"
      },
      {
        "id": "link14",
        "source": "R",
        "target": "flow4"
      },
      {
        "id": "link15",
        "source": "cgamma",
        "target": "flow4"
      },
      {
        "id": "link16",
        "source": "hosp",
        "target": "flow4"
      },
      {
        "id": "link17",
        "source": "H",
        "target": "flow5"
      },
      {
        "id": "link18",
        "source": "R",
        "target": "flow5"
      },
      {
        "id": "link19",
        "source": "death",
        "target": "flow5"
      },
      {
        "id": "link20",
        "source": "los",
        "target": "flow5"
      },
      {
        "id": "link21",
        "source": "H",
        "target": "flow6"
      },
      {
        "id": "link22",
        "source": "D",
        "target": "flow6"
      },
      {
        "id": "link23",
        "source": "death",
        "target": "flow6"
      },
      {
        "id": "link24",
        "source": "los",
        "target": "flow6"
      }
    ]
  },
  "semantics": {
    "ode": {
      "parameters": [
        {
          "id": "p_cbeta",
          "name": "p_cbeta",
          "description": "transmission rate",
          "value": 0.35,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 0.25,
              "maximum": 0.45
            }
          }
        },
        {
          "id": "p_N",
          "name": "p_N",
          "description": "overall population",
          "value": 1001
        },
        {
          "id": "p_cdelta",
          "name": "p_cdelta",
          "description": "latency period",
          "value": 0.2,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 0.1,
              "maximum": 0.3
            }
          }
        },
        {
          "id": "p_cgamma",
          "name": "p_cgamma",
          "description": "infectiousness period",
          "value": 0.2,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 0.1,
              "maximum": 0.3
            }
          }
        },
        {
          "id": "p_death",
          "name": "p_death",
          "description": "death rate of hospitalized",
          "value": 0.08,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 0.01,
              "maximum": 0.1
            }
          }
        },
        {
          "id": "p_hosp",
          "name": "p_hosp",
          "description": "hospitalization rate of infectious",
          "value": 0.1,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 0.01,
              "maximum": 0.2
            }
          }
        },
        {
          "id": "p_los",
          "name": "p_los",
          "description": "hospitalization length of stay",
          "value": 7.0,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 5.0,
              "maximum": 9.0
            }
          }
        },
        {
          "id": "S0",
          "name": "S₀",
          "description": "Total susceptible population at timestep 0",
          "value": 1000
        },
        {
          "id": "E0",
          "name": "E₀",
          "description": "Total exposed population at timestep 0",
          "value": 0
        },
        {
          "id": "I0",
          "name": "I₀",
          "description": "Total infected population at timestep 0",
          "value": 3.0,
          "distribution": {
            "type": "Uniform1",
            "parameters": {
              "minimum": 1.0,
              "maximum": 10.0
            }
          }
        },
        {
          "id": "R0",
          "name": "R₀",
          "description": "Total recovered population at timestep 0",
          "value": 0
        },
        {
          "id": "H0",
          "name": "H₀",
          "description": "Total hospitalized population at timestep 0",
          "value": 0
        },
        {
          "id": "D0",
          "name": "D₀",
          "description": "Total deceased population at timestep 0",
          "value": 0
        }
      ],
      "initials": [
        {
          "target": "S",
          "expression": "p_N - I0",
          "expression_mathml": "<apply><minus/><ci>p_N</ci><ci>I0</ci></apply>"
        },
        {
          "target": "E",
          "expression": "E0",
          "expression_mathml": "<ci>E0</ci>"
        },
        {
          "target": "I",
          "expression": "I0",
          "expression_mathml": "<ci>I0</ci>"
        },
        {
          "target": "R",
          "expression": "R0",
          "expression_mathml": "<ci>R0</ci>"
        },
        {
          "target": "H",
          "expression": "H0",
          "expression_mathml": "<ci>H0</ci>"
        },
        {
          "target": "D",
          "expression": "D0",
          "expression_mathml": "<ci>D0</ci>"
        }
      ],
      "observables": [
        {
          "id": "I",
          "name": "infected",
          "expression": "I",
          "expression_mathml": "<ci>I</ci>"
        },
        {
          "id": "H",
          "name": "hospitalized",
          "expression": "H",
          "expression_mathml": "<ci>H</ci>"
        }
      ]
    }
  }
}