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

Laguzet, Laetitia; Turinici, Gabriel

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

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