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Global optimal vaccination in the SIR model: Properties of the value function and application to cost-effectiveness analysis

Laguzet, Laetitia; Turinici, Gabriel (2015), Global optimal vaccination in the SIR model: Properties of the value function and application to cost-effectiveness analysis, Mathematical Biosciences, 263, p. 180-197. 10.1016/j.mbs.2015.03.002

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-00966622
Date
2015
Journal name
Mathematical Biosciences
Volume
263
Publisher
Elsevier
Published in
Paris
Pages
180-197
Publication identifier
10.1016/j.mbs.2015.03.002
Metadata
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Author(s)
Laguzet, Laetitia

Turinici, Gabriel cc
Abstract (EN)
This paper focuses on optimal vaccination policies for a SIR model; the total cost of the disease is optimized with respect to the cost of a vaccination strategy. We show that the value function is the unique viscosity solution of a HJB equation. This allows to nd the global optimal vaccination policy. At odds with existing literature, it is seen that the value function is not always smooth (sometimes only Lipschitz) and the optimal vaccination policies are not unique. Moreover we rigorously analyze the situation when vaccination can be modeled as instantaneous (with respect to the time evolution of the epidemic) and identify the global optimum solutions.
Subjects / Keywords
vaccination region; optimal vaccination; SIR model; immunization region

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