Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic
In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions ( e.g . physical or social d...
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| Published in | PLoS computational biology Vol. 17; no. 3; p. e1008776 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
04.03.2021
PLOS Public Library of Science (PLoS) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1553-7358 1553-734X 1553-7358 |
| DOI | 10.1371/journal.pcbi.1008776 |
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| Abstract | In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (
e.g
. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. |
|---|---|
| AbstractList | In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. While much remains unknown about the COVID-19 epidemics, evidence to date suggests that mortality among people who have been tested positive for the coronavirus is substantially higher at older ages and near zero for young children [3, 21]. [...]the infectiousness of an individual has been reported to vary as a function of time since infection [22], which is known to affect epidemic spread [23–26]. [...]we compare the performance of optimal control in terms of deaths and hospitalizations for different costs of the control measure. [...]we compare our optimal control strategy to two other strategies that use the same amount of resources to control the outbreak. [...]the average latency from exposed to asymptomatic (ilat) is simply mentioned to define the average time to infectiousness onset (isympt), and also to help the readers to understand the model flow diagram (Fig 1). In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been infected for. The latter allows to take into account the variation of infectiousness as a function of time since infection. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. social distancing) are of great importance to mitigate the pandemic. We propose a model with a double continuous structure by host age and time since infection. By applying optimal control theory to our age-structured model, we identify a solution minimizing deaths and costs associated with the implementation of the control strategy itself. This strategy depends on the age heterogeneity between individuals and consists in a relatively high isolation intensity over the older populations during a hundred days, followed by a steady decrease in a way that depends on the cost associated to a such control. The isolation of the younger population is weaker and occurs only if the cost associated with the control is relatively low. We show that the optimal control strategy strongly outperforms other strategies such as uniform constant control over the whole populations or over its younger fraction. These results bring new facts the debate about age-based control interventions and open promising avenues of research, for instance of age-based contact tracing. In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions ( e.g . physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions ( e.g . physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing. COVID-19 infected individuals differ in the way they spread the infection depending on their age or on the number of days elapsed since the contamination. This individual heterogeneity can impact the design of public health control measures to contain epidemics. Using optimal control theory, we identify a strategy that minimizes deaths and costs due to the implementation of the control measures themselves. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). This strategy consists in rapidly intervening in older populations to protect the older people during the initial phase of the epidemic and (if the cost is intermediate or low) to control the epidemic, before progressively alleviating this control. Interventions in the younger population can occur later if the cost associated with the intervention is low. Such interventions targeted at younger people aim at suppressing the epidemic. While much remains unknown about the COVID-19 epidemics, evidence to date suggests that mortality among people who have been tested positive for the coronavirus is substantially higher at older ages and near zero for young children [3, 21]. [...]the infectiousness of an individual has been reported to vary as a function of time since infection [22], which is known to affect epidemic spread [23–26]. [...]we compare the performance of optimal control in terms of deaths and hospitalizations for different costs of the control measure. [...]we compare our optimal control strategy to two other strategies that use the same amount of resources to control the outbreak. [...]the average latency from exposed to asymptomatic (ilat) is simply mentioned to define the average time to infectiousness onset (isympt), and also to help the readers to understand the model flow diagram (Fig 1). |
| Audience | Academic |
| Author | Choisy, Marc Sofonea, Mircea T. Richard, Quentin Alizon, Samuel Djidjou-Demasse, Ramsès |
| AuthorAffiliation | 1 MIVEGEC, Univ. Montpellier, IRD, CNRS, Montpellier, France Stony Brook University, UNITED STATES 2 Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, United Kingdom 3 Oxford University Clinical Research Unit, Ho Chi Minh, Vietnam |
| AuthorAffiliation_xml | – name: 3 Oxford University Clinical Research Unit, Ho Chi Minh, Vietnam – name: 1 MIVEGEC, Univ. Montpellier, IRD, CNRS, Montpellier, France – name: 2 Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, United Kingdom – name: Stony Brook University, UNITED STATES |
| Author_xml | – sequence: 1 givenname: Quentin orcidid: 0000-0003-2450-3350 surname: Richard fullname: Richard, Quentin – sequence: 2 givenname: Samuel orcidid: 0000-0002-0779-9543 surname: Alizon fullname: Alizon, Samuel – sequence: 3 givenname: Marc orcidid: 0000-0002-5187-6390 surname: Choisy fullname: Choisy, Marc – sequence: 4 givenname: Mircea T. orcidid: 0000-0002-4499-0435 surname: Sofonea fullname: Sofonea, Mircea T. – sequence: 5 givenname: Ramsès orcidid: 0000-0003-1684-5190 surname: Djidjou-Demasse fullname: Djidjou-Demasse, Ramsès |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33661890$$D View this record in MEDLINE/PubMed https://hal.science/hal-02879512$$DView record in HAL |
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| Copyright | COPYRIGHT 2021 Public Library of Science 2021 Richard et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. Distributed under a Creative Commons Attribution 4.0 International License 2021 Richard et al 2021 Richard et al |
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| Keywords | COVID-19 Age-structured model Outbreak Age of infection Epidemiology Optimal control |
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| PublicationDate_xml | – month: 03 year: 2021 text: 2021-03-04 day: 04 |
| PublicationDecade | 2020 |
| PublicationPlace | United States |
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| PublicationTitle | PLoS computational biology |
| PublicationTitleAlternate | PLoS Comput Biol |
| PublicationYear | 2021 |
| Publisher | Public Library of Science PLOS Public Library of Science (PLoS) |
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| Snippet | In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for.... While much remains unknown about the COVID-19 epidemics, evidence to date suggests that mortality among people who have been tested positive for the... In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been... |
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| Title | Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic |
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