COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
Identifieur interne : 000087 ( Hal/Corpus ); précédent : 000086; suivant : 000088COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
Auteurs : Arthur Charpentier ; Romuald Elie ; Mathieu Laurière ; Viet-Chi TranSource :
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Abstract
We consider here an extended $SIR$ model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the subtle trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition phase to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario hereby avoids the second wave of infection, provided the lockdown is released sufficiently slowly. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.
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<front><div type="abstract" xml:lang="en"> <p>We consider here an extended $SIR$ model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the subtle trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition phase to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario hereby avoids the second wave of infection, provided the lockdown is released sufficiently slowly. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.</p>
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<sourceDesc> <biblStruct> <analytic> <title xml:lang="en">COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability</title>
<author role="aut"> <persName> <forename type="first">Arthur</forename>
<surname>Charpentier</surname>
</persName>
<email type="md5">4f44db78857a92f843bdd4a0a0a598e7</email>
<email type="domain">univ-rennes1.fr</email>
<idno type="idhal" notation="string">arthur-charpentier</idno>
<idno type="idhal" notation="numeric">5493</idno>
<idno type="halauthorid">356401</idno>
<affiliation ref="#struct-360045"></affiliation>
</author>
<author role="aut"> <persName> <forename type="first">Romuald</forename>
<surname>Elie</surname>
</persName>
<idno type="halauthorid">73525</idno>
<affiliation ref="#struct-1004422"></affiliation>
</author>
<author role="aut"> <persName> <forename type="first">Mathieu</forename>
<surname>Laurière</surname>
</persName>
<email type="md5">545c7ff1e8be861b81d97e93c3248d69</email>
<email type="domain">gmail.com</email>
<idno type="halauthorid">1014870</idno>
<affiliation ref="#struct-171622"></affiliation>
</author>
<author role="aut"> <persName> <forename type="first">Viet-Chi</forename>
<surname>Tran</surname>
</persName>
<email type="md5">bf846b500b47737539728d5f17b9796a</email>
<email type="domain">u-pem.fr</email>
<idno type="idhal" notation="string">tranvietchi</idno>
<idno type="idhal" notation="numeric">165</idno>
<idno type="halauthorid">1195452</idno>
<affiliation ref="#struct-1004422"></affiliation>
</author>
</analytic>
<monogr> <imprint></imprint>
</monogr>
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<profileDesc> <langUsage> <language ident="en">English</language>
</langUsage>
<textClass> <keywords scheme="author"> <term xml:lang="en">COVID-19</term>
<term xml:lang="en">Optimal Control</term>
<term xml:lang="en">Lockdown</term>
<term xml:lang="en">Testing</term>
<term xml:lang="en">Intensive Care Unit (ICU)</term>
<term xml:lang="en">SARS-CoV-2</term>
<term xml:lang="en">Sustainability</term>
<term xml:lang="en">Detection</term>
<term xml:lang="en">Quarantine</term>
</keywords>
<classCode scheme="classification">49N90, 92D30, 34H05</classCode>
<classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
<classCode scheme="halDomain" n="math.math-pr">Mathematics [math]/Probability [math.PR]</classCode>
<classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
</textClass>
<abstract xml:lang="en"> <p>We consider here an extended $SIR$ model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care unit (ICU) capacity. Our model enables a tractable quantitative analysis of the optimal policy for the control of the epidemic dynamics using both lockdown and detection intervention levers. With parametric specification based on literature on COVID-19, we investigate the sensitivities of various quantities on the optimal strategies, taking into account the subtle trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. We identify the optimal lockdown policy as an intervention structured in 4 successive phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition phase to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario hereby avoids the second wave of infection, provided the lockdown is released sufficiently slowly. We also provide optimal intervention measures with increasing ICU capacity, as well as optimization over the effort on detection of infectious and immune individuals. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.</p>
</abstract>
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