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Oliveira_NatCommun2021_model.xml
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<?xml version='1.0' encoding='UTF-8'?>
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<notes>
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<pre>Oliveira, Nature 2021.
https://www.nature.com/articles/s41467-020-19798-3.
COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase inR0. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses.
To model with a two-step transmission rate, set 'beta_2_multiplier' = 0. To model with a three-step transmission rate, set 'beta_2_multiplier' = 1.
</pre>
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<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:29:17Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI12" id="delta_" name="delta_" value="0.6951361054" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI12">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:32:23Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI13" id="p_symp_rate" name="p_symp_rate" value="0.2" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI13">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:32:57Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI14" id="kappa" name="kappa" value="0.25" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI14">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:33:06Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI15" id="gamma_a" name="gamma_a" value="0.285714" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI15">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:33:20Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI16" id="gamma_s" name="gamma_s" value="0.25" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI16">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:34:03Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI17" id="h_hosp_rate" name="h_hosp_rate" value="0" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI17">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:34:18Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI18" id="xi" name="xi" value="0.53" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI18">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:35:44Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI19" id="gamma_h" name="gamma_h" value="0.131351606436" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI19">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:36:03Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI20" id="gamma_u" name="gamma_u" value="0.1870201755885" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI20">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:36:46Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI21" id="mu_h" name="mu_h" value="0.15" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI21">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:37:04Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI22" id="mu_u" name="mu_u" value="0.4" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI22">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:37:20Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI23" id="omega_h" name="omega_h" value="0.14" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI23">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:37:31Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI24" id="omega_u" name="omega_u" value="0.29" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI24">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:37:39Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI25" id="beta_0" name="beta_0" value="0.807194090959563" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI25">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:40:41Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI26" id="beta_1" name="beta_1" value="0.560641488770886" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI26">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:40:47Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI27" id="beta_2" name="beta_2" value="0.66" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI27">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:40:54Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI28" id="t_1" name="t_1" value="23.4530530945" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI28">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:41:00Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI29" id="t_2" name="t_2" value="97" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI29">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T14:41:06Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI30" id="beta" name="beta" value="0.807194090959563" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI30">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:00:31Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI31" id="exposed_to_asymptomatic" name="exposed_to_asymptomatic" value="0.2" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI31">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:18:58Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI32" id="exposed_to_symptomatic" name="exposed_to_symptomatic" value="0.05" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI32">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:23:46Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI33" id="symptomatic_to_recovered" name="symptomatic_to_recovered" value="0.25" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI33">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:35:47Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI34" id="symptomatic_to_hospitalized" name="symptomatic_to_hospitalized" value="0" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI34">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:38:27Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI35" id="symptomatic_to_icu" name="symptomatic_to_icu" value="0" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI35">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:38:32Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI36" id="hospitalized_to_recovered" name="hospitalized_to_recovered" value="0.096018024304716" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI36">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:41:17Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI37" id="hospitalized_to_icu" name="hospitalized_to_icu" value="0.01838922490104" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI37">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:43:48Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI38" id="hospitalized_to_deaths" name="hospitalized_to_deaths" value="0.016944357230244" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI38">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:47:46Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI39" id="icu_to_deaths" name="icu_to_deaths" value="0.053113729867134" constant="false">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI39">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-22T15:47:58Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI40" id="exposed_init_concentration" name="exposed_init_concentration" value="2.24673170025082e-06" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI40">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-30T08:38:24Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI41" id="asymptomatic_init_concentration" name="asymptomatic_init_concentration" value="6.4828815498309e-07" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI41">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-30T08:38:50Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI42" id="symptomatic_init_concentration" name="symptomatic_init_concentration" value="1.99259135560373e-06" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI42">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-03-30T08:39:05Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
<parameter metaid="COPASI43" id="beta_2_multiplier" name="beta_2_multiplier" value="1" constant="true">
<annotation>
<COPASI xmlns="http://www.copasi.org/static/sbml">
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#COPASI43">
<dcterms:created>
<rdf:Description>
<dcterms:W3CDTF>2021-05-03T14:28:51Z</dcterms:W3CDTF>
</rdf:Description>
</dcterms:created>
</rdf:Description>
</rdf:RDF>
</COPASI>
</annotation>
</parameter>
</listOfParameters>
<listOfInitialAssignments>
<initialAssignment symbol="Exposed">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> exposed_init_concentration </ci>
<ci> population </ci>
</apply>
</math>
</initialAssignment>
<initialAssignment symbol="Susceptible">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> population </ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn> 1 </cn>
<ci> asymptomatic_init_concentration </ci>
</apply>
<ci> exposed_init_concentration </ci>
</apply>
<ci> symptomatic_init_concentration </ci>
</apply>
</apply>
</math>
</initialAssignment>
<initialAssignment symbol="Asymptomatic">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> asymptomatic_init_concentration </ci>
<ci> population </ci>
</apply>
</math>
</initialAssignment>
<initialAssignment symbol="Symptomatic">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> symptomatic_init_concentration </ci>
<ci> population </ci>
</apply>
</math>
</initialAssignment>
<initialAssignment symbol="Cumulative_cases">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> symptomatic_init_concentration </ci>
<ci> population </ci>
</apply>
</math>
</initialAssignment>
</listOfInitialAssignments>
<listOfRules>
<assignmentRule variable="beta">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<piecewise>
<piece>
<ci> beta_0 </ci>
<apply>
<lt/>
<csymbol encoding="text" definitionURL="http://www.sbml.org/sbml/symbols/time"> time </csymbol>
<ci> t_1 </ci>
</apply>
</piece>
<otherwise>
<piecewise>
<piece>
<ci> beta_1 </ci>
<apply>
<lt/>
<csymbol encoding="text" definitionURL="http://www.sbml.org/sbml/symbols/time"> time </csymbol>
<ci> t_2 </ci>
</apply>
</piece>
<otherwise>
<apply>
<plus/>
<apply>
<times/>
<ci> beta_2 </ci>
<ci> beta_2_multiplier </ci>
</apply>
<apply>
<times/>
<ci> beta_1 </ci>
<apply>
<minus/>
<cn> 1 </cn>
<ci> beta_2_multiplier </ci>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</otherwise>
</piecewise>
</math>
</assignmentRule>
<assignmentRule variable="exposed_to_asymptomatic">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> kappa </ci>
<apply>
<minus/>
<cn> 1 </cn>
<ci> p_symp_rate </ci>
</apply>
</apply>
</math>
</assignmentRule>
<assignmentRule variable="exposed_to_symptomatic">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> kappa </ci>
<ci> p_symp_rate </ci>
</apply>
</math>
</assignmentRule>
<assignmentRule variable="symptomatic_to_recovered">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<apply>
<minus/>
<cn> 1 </cn>
<ci> h_hosp_rate </ci>
</apply>
<ci> gamma_s </ci>
</apply>
</math>
</assignmentRule>
<assignmentRule variable="symptomatic_to_hospitalized">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> h_hosp_rate </ci>
<ci> xi </ci>
<ci> gamma_s </ci>
</apply>
</math>
</assignmentRule>
<assignmentRule variable="symptomatic_to_icu">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci> h_hosp_rate </ci>
<apply>
<minus/>
<cn> 1 </cn>
<ci> xi </ci>
</apply>
<ci> gamma_s </ci>
</apply>
</math>
</assignmentRule>
<assignmentRule variable="hospitalized_to_recovered">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<apply>
<minus/>
<cn> 1 </cn>
<ci> omega_h </ci>
</apply>
<apply>
<minus/>
<cn> 1 </cn>
<ci> mu_h </ci>
</apply>