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Optimal vaccination in a SIRS epidemic model

We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible indiv...

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Autores principales: Federico, Salvatore, Ferrari, Giorgio, Torrente, Maria-Laura
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9770565/
https://www.ncbi.nlm.nih.gov/pubmed/36573250
http://dx.doi.org/10.1007/s00199-022-01475-9
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author Federico, Salvatore
Ferrari, Giorgio
Torrente, Maria-Laura
author_facet Federico, Salvatore
Ferrari, Giorgio
Torrente, Maria-Laura
author_sort Federico, Salvatore
collection PubMed
description We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton–Jacobi–Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of Regular Lagrangian Flows. From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small.
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spelling pubmed-97705652022-12-22 Optimal vaccination in a SIRS epidemic model Federico, Salvatore Ferrari, Giorgio Torrente, Maria-Laura Econ Theory Research Article We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton–Jacobi–Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of Regular Lagrangian Flows. From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small. Springer Berlin Heidelberg 2022-12-21 /pmc/articles/PMC9770565/ /pubmed/36573250 http://dx.doi.org/10.1007/s00199-022-01475-9 Text en © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Research Article
Federico, Salvatore
Ferrari, Giorgio
Torrente, Maria-Laura
Optimal vaccination in a SIRS epidemic model
title Optimal vaccination in a SIRS epidemic model
title_full Optimal vaccination in a SIRS epidemic model
title_fullStr Optimal vaccination in a SIRS epidemic model
title_full_unstemmed Optimal vaccination in a SIRS epidemic model
title_short Optimal vaccination in a SIRS epidemic model
title_sort optimal vaccination in a sirs epidemic model
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9770565/
https://www.ncbi.nlm.nih.gov/pubmed/36573250
http://dx.doi.org/10.1007/s00199-022-01475-9
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