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
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-00966622
Journal nameMathematical Biosciences
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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 / Keywordsvaccination region; optimal vaccination; SIR model; immunization region
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