Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection
We analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and durability of protection. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a no...
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| Language: | English |
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AIMS Press
2018-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018028 |
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| author | Francesco Salvarani Gabriel Turinici |
| author_facet | Francesco Salvarani Gabriel Turinici |
| author_sort | Francesco Salvarani |
| collection | DOAJ |
| description | We analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and durability of protection. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a novel numerical method to find the equilibrium. Various issues of the model are then discussed, such as the dependence of the optimal policy with respect to the imperfections of the vaccine, as well as the best vaccination timing. The numerical results show that, under specific circumstances, some counter-intuitive behaviors are optimal, such as, for example, an increase of the fraction of vaccinated individuals when the efficacy of the vaccine is decreasing up to a threshold. The possibility of finding optimal strategies at the individual level can help public health decision makers in designing efficient vaccination campaigns and policies. |
| format | Article |
| id | doaj-art-f9b90b0557c04cb7a475b5242cef038c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f9b90b0557c04cb7a475b5242cef038c2025-01-24T02:40:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-05-0115362965210.3934/mbe.2018028Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protectionFrancesco Salvarani0Gabriel Turinici1Université Paris-Dauphine, PSL Research University, CNRS UMR 7534, CEREMADE, 75016 Paris, France, & Università degli Studi di Pavia, Dipartimento di Matematica, 27100 Pavia, Italy,Université Paris-Dauphine, PSL Research University, CNRS UMR 7534, CEREMADE, 75016 Paris, France, & Institut Universitaire de France, Paris, FranceWe analyze a model of agent based vaccination campaign against influenza with imperfect vaccine efficacy and durability of protection. We prove the existence of a Nash equilibrium by Kakutani's fixed point theorem in the context of non-persistent immunity. Subsequently, we propose and test a novel numerical method to find the equilibrium. Various issues of the model are then discussed, such as the dependence of the optimal policy with respect to the imperfections of the vaccine, as well as the best vaccination timing. The numerical results show that, under specific circumstances, some counter-intuitive behaviors are optimal, such as, for example, an increase of the fraction of vaccinated individuals when the efficacy of the vaccine is decreasing up to a threshold. The possibility of finding optimal strategies at the individual level can help public health decision makers in designing efficient vaccination campaigns and policies.https://www.aimspress.com/article/doi/10.3934/mbe.2018028mean field gamessir modelvaccination persistencedurability of protectionlimited immunityvaccine effectivenessinfluenza |
| spellingShingle | Francesco Salvarani Gabriel Turinici Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection Mathematical Biosciences and Engineering mean field games sir model vaccination persistence durability of protection limited immunity vaccine effectiveness influenza |
| title | Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| title_full | Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| title_fullStr | Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| title_full_unstemmed | Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| title_short | Optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| title_sort | optimal individual strategies for influenza vaccines with imperfect efficacy and durability of protection |
| topic | mean field games sir model vaccination persistence durability of protection limited immunity vaccine effectiveness influenza |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018028 |
| work_keys_str_mv | AT francescosalvarani optimalindividualstrategiesforinfluenzavaccineswithimperfectefficacyanddurabilityofprotection AT gabrielturinici optimalindividualstrategiesforinfluenzavaccineswithimperfectefficacyanddurabilityofprotection |