Location: SEIR @ b973009caf43 / COVIDSim_Q.cellml
- Author:
- Soroush <ssaf006@aucklanduni.ac.nz>
- Date:
- 2020-04-05 22:21:32+12:00
- Desc:
- added the quarantine component
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/5d4/rawfile/b973009caf430b1636cfd1133a23bfd570a85691/COVIDSim_Q.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="COVID_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="day">
<unit multiplier="86400" units="second"/>
</units>
<units name="per_day">
<unit exponent="-1" multiplier="86400" units="second"/>
</units>
<component name="environment">
<variable name="time" public_interface="out" units="day"/>
</component>
<component name="main">
<!--/////////////// Variables /////////////////-->
<variable name="t" public_interface="in" units="day"/>
<!-- Susceptible-->
<variable initial_value="0.999996" name="S" units="dimensionless"/>
<!-- Exposed-->
<variable initial_value="0.000004" name="E" units="dimensionless"/>
<!-- Pre-Symptomatic-->
<variable initial_value="0" name="I_p" units="dimensionless"/>
<!-- Quarantined-->
<variable initial_value="0" name="Q" units="dimensionless"/>
<!-- Infectious, untested-->
<variable initial_value="0" name="I_u" units="dimensionless"/>
<!-- Infectious, tested-->
<variable initial_value="0" name="I_t" units="dimensionless"/>
<!-- Infectious, total-->
<variable name="I" units="dimensionless"/>
<!-- Recovered, untested-->
<variable initial_value="0" name="R_u" units="dimensionless"/>
<!-- Recovered, tested-->
<variable initial_value="0" name="R_t" units="dimensionless"/>
<!-- Recovered from Quarantined-->
<variable initial_value="0" name="R_q" units="dimensionless"/>
<!-- Recovered, total-->
<variable name="R" units="dimensionless"/>
<!-- Deaths-->
<variable name="D" units="dimensionless"/>
<!-- Population Size-->
<variable initial_value="5000000" name="N" units="dimensionless"/>
<!-- Infection Fatality Rate-->
<variable name="IFR" units="dimensionless"/>
<!--/////////////// Parameters /////////////////-->
<!-- Infection Fatality Rate (when ICU is under max capacity)-->
<variable initial_value="0.01" name="IFR_0" units="dimensionless"/>
<!-- Infection Fatality Rate (for infectious exceeding ICU capacity)-->
<variable initial_value="0.02" name="IFR_1" units="dimensionless"/>
<!-- Transmission Coefficient-->
<variable name="beta" units="per_day"/>
<!-- Relative Infectiousness in Pre-Symptomatic Period-->
<variable initial_value="0.15" name="epsilon" units="dimensionless"/>
<!-- E->P Transition Rate-->
<variable initial_value="0.25" name="alpha" units="per_day"/>
<!-- P->I Transition Rate-->
<variable initial_value="1.0" name="delta" units="per_day"/>
<!-- I->R Transition Rate-->
<variable initial_value="0.1" name="gamma" units="per_day"/>
<!-- Testing Rate for Symptomatic Infections-->
<variable initial_value="0.1" name="c" units="per_day"/>
<!-- Estimated ICU Maximum Capacity-->
<variable initial_value="500" name="n_ICU" units="dimensionless"/>
<!-- Proportion of Total Infections Requiring ICU-->
<variable initial_value="0.0125" name="p_ICU" units="dimensionless"/>
<!-- Proportion of Total Infections Requiring Hospitalisation-->
<variable initial_value="0.05" name="p_hosp" units="dimensionless"/>
<!-- Basic Reproduction Number-->
<variable initial_value="2.5" name="R_0" units="dimensionless"/>
<!-- Testing Time-->
<variable initial_value="0.1" name="tt" units="per_day"/>
<!-- Recovery Time in Quarantine-->
<variable initial_value="0.07142" name="rtq" units="per_day"/>
<!--/////////////// System of ODEs /////////////////-->
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>S</ci>
</apply>
<apply>
<times/>
<apply>
<minus/>
<ci>beta</ci>
</apply>
<ci>S</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>epsilon</ci>
<ci>I_p</ci>
</apply>
<ci>I_u</ci>
<ci>I_t</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>E</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta</ci>
<ci>S</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>epsilon</ci>
<ci>I_p</ci>
</apply>
<ci>I_u</ci>
<ci>I_t</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha</ci>
<ci>E</ci>
</apply>
</apply>
<apply>
<times/>
<ci>tt</ci>
<ci>E</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>Q</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>tt</ci>
<ci>E</ci>
</apply>
<apply>
<times/>
<ci>rtq</ci>
<ci>Q</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>R_q</ci>
</apply>
<apply>
<times/>
<ci>rtq</ci>
<ci>Q</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>I_p</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha</ci>
<ci>E</ci>
</apply>
<apply>
<times/>
<ci>delta</ci>
<ci>I_p</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>I_u</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>delta</ci>
<ci>I_p</ci>
</apply>
<apply>
<times/>
<apply>
<plus/>
<ci>gamma</ci>
<ci>c</ci>
</apply>
<ci>I_u</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>I_t</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>c</ci>
<ci>I_u</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<ci>I_t</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>R_u</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>IFR</ci>
</apply>
<ci>I_u</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>t</ci>
</bvar>
<ci>R_t</ci>
</apply>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>IFR</ci>
</apply>
<ci>I_t</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>D</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>S</ci>
</apply>
<ci>E</ci>
</apply>
<ci>I_p</ci>
</apply>
<ci>I_u</ci>
</apply>
<ci>I_t</ci>
</apply>
<ci>R_u</ci>
</apply>
<ci>R_t</ci>
</apply>
<ci>R_q</ci>
</apply>
<ci>Q</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I</ci>
<apply>
<plus/>
<ci>I_t</ci>
<ci>I_u</ci>
<ci>I_p</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>R</ci>
<apply>
<plus/>
<ci>R_t</ci>
<ci>R_u</ci>
<ci>R_q</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>beta</ci>
<apply>
<divide/>
<ci>R_0</ci>
<apply>
<plus/>
<apply>
<divide/>
<ci>epsilon</ci>
<ci>delta</ci>
</apply>
<apply>
<divide/>
<cn cellml:units="dimensionless">1</cn>
<ci>gamma</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>IFR</ci>
<piecewise>
<piece>
<ci>IFR_0</ci>
<apply>
<leq/>
<apply>
<times/>
<ci>N</ci>
<ci>I</ci>
<ci>p_ICU</ci>
</apply>
<ci>n_ICU</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<ci>IFR_1</ci>
<apply>
<times/>
<apply>
<divide/>
<ci>n_ICU</ci>
<apply>
<times/>
<ci>N</ci>
<ci>I</ci>
<ci>p_ICU</ci>
</apply>
</apply>
<apply>
<minus/>
<ci>IFR_1</ci>
<ci>IFR_0</ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="main" component_2="environment"/>
<map_variables variable_1="t" variable_2="time"/>
</connection>
</model>