Asymptotic analysis of optimal vaccination policies
Targeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivatio...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2023
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| _version_ | 1797108755061538816 |
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| author | Penn, MJ Donnelly, C |
| author_facet | Penn, MJ Donnelly, C |
| author_sort | Penn, MJ |
| collection | OXFORD |
| description | Targeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivation of the leading-order optimal vaccination policy under multi-group susceptible–infected–recovered dynamics in two different cases. Firstly, it considers the case of a small vulnerable subgroup in a population and shows that (in the asymptotic limit) it is optimal to vaccinate this group first, regardless of the properties of the other groups. Then, it considers the case of a small vaccine supply and transforms the optimal vaccination problem into a simple knapsack problem by linearising the final size equations. Both of these cases are then explored further through numerical examples, which show that these solutions are also directly useful for realistic parameter values. Moreover, the findings of this paper give some general principles for optimal vaccination policies which will help policy-makers and the public to understand the reasoning behind optimal vaccination programs in more generic cases. |
| first_indexed | 2024-03-07T07:32:55Z |
| format | Journal article |
| id | oxford-uuid:1a7c4958-f8e8-464d-abb1-02d2ba57ff79 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:32:55Z |
| publishDate | 2023 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:1a7c4958-f8e8-464d-abb1-02d2ba57ff792023-02-10T08:08:45ZAsymptotic analysis of optimal vaccination policiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1a7c4958-f8e8-464d-abb1-02d2ba57ff79EnglishSymplectic ElementsSpringer2023Penn, MJDonnelly, CTargeted vaccination policies can have a significant impact on the number of infections and deaths in an epidemic. However, optimising such policies is complicated, and the resultant solution may be difficult to explain to policy-makers and to the public. The key novelty of this paper is a derivation of the leading-order optimal vaccination policy under multi-group susceptible–infected–recovered dynamics in two different cases. Firstly, it considers the case of a small vulnerable subgroup in a population and shows that (in the asymptotic limit) it is optimal to vaccinate this group first, regardless of the properties of the other groups. Then, it considers the case of a small vaccine supply and transforms the optimal vaccination problem into a simple knapsack problem by linearising the final size equations. Both of these cases are then explored further through numerical examples, which show that these solutions are also directly useful for realistic parameter values. Moreover, the findings of this paper give some general principles for optimal vaccination policies which will help policy-makers and the public to understand the reasoning behind optimal vaccination programs in more generic cases. |
| spellingShingle | Penn, MJ Donnelly, C Asymptotic analysis of optimal vaccination policies |
| title | Asymptotic analysis of optimal vaccination policies |
| title_full | Asymptotic analysis of optimal vaccination policies |
| title_fullStr | Asymptotic analysis of optimal vaccination policies |
| title_full_unstemmed | Asymptotic analysis of optimal vaccination policies |
| title_short | Asymptotic analysis of optimal vaccination policies |
| title_sort | asymptotic analysis of optimal vaccination policies |
| work_keys_str_mv | AT pennmj asymptoticanalysisofoptimalvaccinationpolicies AT donnellyc asymptoticanalysisofoptimalvaccinationpolicies |