Globally optimal vaccination policies in the SIR model: smoothness of the value function and uniqueness of the optimal strategies

Laetitia Laguzet (1) , Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: optimal vaccination; SIR model; vaccination region; immunization region

Domaines: Optimisation et contrôle [math.OC]; Santé publique et épidémiologie; Maladies infectieuses

Laetitia Laguzet, Gabriel Turinici. Globally optimal vaccination policies in the SIR model: smoothness of the value function and uniqueness of the optimal strategies. 2014. ⟨hal-00966622v1⟩