Location: SEIR @ 856cf169513b / COVIDSim.cellml

Author:
GitHub <noreply@github.com>
Date:
2020-04-07 11:19:26+12:00
Desc:
Merge pull request #1 from ssafaei/master SEIR original model
Permanent Source URI:
https://models.physiomeproject.org/workspace/5d5/rawfile/856cf169513b2b1a57843cb5feef01aed762d480/COVIDSim.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="P" 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, 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"/>
        <!--/////////////// 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>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>
                        <times/>
                        <ci>beta</ci>
                        <ci>S</ci>
                        <apply>
                            <plus/>
                            <apply>
                                <times/>
                                <ci>epsilon</ci>
                                <ci>P</ci>
                            </apply>
                            <ci>I_u</ci>
                            <ci>I_t</ci>
                        </apply>
                    </apply>
                    <apply>
                        <times/>
                        <ci>alpha</ci>
                        <ci>E</ci>
                    </apply>
                </apply>
            </apply>
            <apply>
                <eq/>
                <apply>
                    <diff/>
                    <bvar>
                        <ci>t</ci>
                    </bvar>
                    <ci>P</ci>
                </apply>
                <apply>
                    <minus/>
                    <apply>
                        <times/>
                        <ci>alpha</ci>
                        <ci>E</ci>
                    </apply>
                    <apply>
                        <times/>
                        <ci>delta</ci>
                        <ci>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>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/>
                                            <cn cellml:units="dimensionless">1</cn>
                                            <ci>S</ci>
                                        </apply>
                                        <ci>E</ci>
                                    </apply>
                                    <ci>P</ci>
                                </apply>
                                <ci>I_u</ci>
                            </apply>
                            <ci>I_t</ci>
                        </apply>
                        <ci>R_u</ci>
                    </apply>
                    <ci>R_t</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>I</ci>
                <apply>
                    <plus/>
                    <ci>I_t</ci>
                    <ci>I_u</ci>
                </apply>
            </apply>
            <apply>
                <eq/>
                <ci>R</ci>
                <apply>
                    <plus/>
                    <ci>R_t</ci>
                    <ci>R_u</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>